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Nikulin Viacheslav Valentinovich

Total publications: 90 (84)
in MathSciNet: 75 (69)
in zbMATH: 72 (67)
in Web of Science: 47 (41)
in Scopus: 40 (40)
Cited articles: 72
Citations in Math-Net.Ru: 483
Citations in Web of Science: 1253
Citations in Scopus: 653
Presentations: 19

Number of views:
This page:4160
Abstract pages:16365
Full texts:5497
References:1008
Nikulin Viacheslav Valentinovich
Professor
Doctor of physico-mathematical sciences (1985)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: , ,
Website: http://vnikulin.com
Keywords: K3 surface, Calabi–Yau manifold, mirror symmetry, Picard lattice, automorphism group, integral quadratic form, real algebraic geometry, hyperbolic reflection group, hyperbolic Kac–Moody algebra, Borcherds algebra, automorphic form.
UDC: 511.334, 512.542, 512.647.2, 512.774, 512.774.2, 512.774.4, 512.817.72, 512.818.4, 513.6, 511, 512.723, 512.817.6, 512.734, 519.46, 512.7, 512.774.5, 511.3, 511.6, 512.747, 512.647.4

Subject:

Algebraic geometry, mirror symmetry, arithmetic of quadratic forms, hyperbolic reflection groups, hyperbolic Kac–Moody algebras.

Biography

I was born 1950 in Kirov, Russia. 1965–1967, I was a student of Physical-Mathematical school No. 18 under MGU. 1967–1972, I was a student of Mechanical-Mathematical Department of MGU. 1972–1975, I was a graduate student of MIAN of Steklov under supervision by I.R. Shafarevich.

In 1977, I defended PhD thesis "Finite automorphism groups of Kahlerian K3 surfaces" (was published in 1979 in Proceed. of Moscow Math. Soc.). A general theory of such groups was constructed (especially of finite symplectic automorphism groups), and the classification of Abelian finite symplectic automorphism groups of K3 was given.

In 1979, in the paper "Integral symmetric bilinear forms and some of their geometric applications", I developed the discriminant forms technique for integral symmetric bilinear forms which became very useful in applicaitons. As geometric applications, 1) another approach to finite symplectic automorphism groups of K3 was given; 2) calculation of Milnor quadratic forms of 2-dimensional quasi-homogeneous singularities of functions was given in terms of their resolution, in application to 14 exceptional Arnold's singularities it gave an approach to Arnold's duality for them which was a first example of mirror symmetry; 3) a description of connected components of moduli of real polarized K3 surfaces was given. It is my the most cited paper (more than 100 citations by AMS Math Review).

In papers 1979–1984, I described K3 surfaces with finite automoprhism groups which is equivalent (by Global Torelli Theorem) to description of hyperbolic integral symmetric bilinear forms with automorphism groups generated by 2-reflections up to finite index. It was proved, in particular, that their number is finite in essential. For the rank 4 it was done by Vinberg.

In papers 1980–1981, I generalized above results to arbitrary arithmetic hyperbolic (in Lobachevsky spaces) reflection groups. Finiteness of the number of maximal such groups was proved in dimensions at least 10. Using the developed by me methods, later E.B. Vinberg, M.N. Prokhorov and A.G. Khovansky proved that the dimension of reflection groups in Lobachevsky spaces, with fundamental chambers of finite volume, is absolutely bounded.

In my further papers, the above methods were generalized and applied to different algebraic varieties and related polyhedra (e.g. to Mori polyhedra and nef polyhedra), to hyperbolic Kac–Moody algebras, different types of real algebraic varieties. I shall give more concrete results below.

In 1983–2008 papers, to different types of real algebraic varieties: to curves, surfaces, to description of connected components of moduli of K3 surfaces with different conditions on Picard lattices.

In 1984–2004 papers, to K3 and Enriques surfaces (automorphism groups), to Del Pezzo surfaces with log-terminal singularities, to algebraic surfaces with nef anti-canonical class, to algebraic surfaces with finite polyhedral Mori cone (finiteness results), to 3-dimensional Fano and Calabi–Yau manifolds (bounds on Picard number). Later, to some of these results, some other approaches were found which use Mori theory.

In 1995–2002 papers (most of them together with V.A. Gritsenko), to description and construction of Lorentzian (hyperbolic, generalized) Kac–Moody algebras with denominator identities which are automorphic forms (Borcherds algebras).

In 2003–2011 papers (many of them together with Carlo Madonna) methods of integral symmetric bilinear forms and discriminant forms were applied to description of cases when the moduli space of coherent sheaves with given Mukai vector on a K3 surface is isomorphic to the K3 surface itself which gives an algebraic cycle on the product of K3 with itself (or its self-correspondence).

In 2007–2011 papers, using results by Long, Maclachlan, Reid for 2-dimensional case and Agol for 3-dimensional case, and my old finiteness results and methods of 1981–1982 for arithmetic hyperbolic reflection groups in dimensions greater than 9, these finiteness results were generalized to remaining dimensions 2–8. Moreover, good bounds on ground fields were obtained which gives a hope for complete enumeration of maximal arithmetic hyperbolic refection groups.

In my last 2013 paper, the suggested by me method of 1979 to description of finite symplectic automorphism groups of K3 surfaces was generalized and specialized to concrete Niemeier lattices. This gives, in particular, description of finite symplectic automorphism groups of Kahlerian K3 surfaces together with their non-singular rational curves. This completes the classical results by Mukai, Xiao, Kondo, Hashimoto which were obtained after my 1979 paper.

   
Main publications:
  1. V. Alexeev, V. V. Nikulin, Del Pezzo and $K3$ surfaces, MSJ Memoirs, 15, Mathematical Society of Japan, Tokyo, 2006 , xvi+149 pp.  mathscinet  zmath
  2. V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. II”, Internat. J. Math., 9:2 (1998), 201–275  crossref  mathscinet  zmath  isi
  3. V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. I”, Internat. J. Math., 9:2 (1998), 153–199  crossref  mathscinet  zmath  isi
  4. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi  scopus
  5. V. V. Nikulin, “Konechnye gruppy avtomorfizmov kelerovykh poverkhnostei tipa $K_3$”, Tr. MMO, 38, Izd-vo Mosk. un-ta, M., 1979, 75–137  mathnet  mathscinet  zmath
  6. V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167  mathnet  crossref  mathscinet  zmath  isi  scopus

http://www.mathnet.ru/eng/person8383
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:nikulin.viacheslav-v
https://mathscinet.ams.org/mathscinet/MRAuthorID/211729
http://elibrary.ru/author_items.asp?authorid=5631
http://www.researcherid.com/rid/Q-4462-2016
http://www.scopus.com/authid/detail.url?authorId=55965179900

Full list of publications:
| by years | by types | by times cited | scientific publications | common list |



   2018
1. V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. Math., 82:4 (2018), 752–816  mathnet  crossref  crossref  adsnasa  isi  elib  scopus
2. Valery Gritsenko, Viacheslav V. Nikulin, “Lorentzian Kac–Moody algebras with Weyl groups of 2-reflections”, Proceedings of London Mathematical Society, 116:3 (2018), 485–533  mathnet (cited: 1)  crossref  isi  scopus
3. Viacheslav V. Nikulin, Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with small finite symplectic automorphism groups, 2018 , 39 pp., arXiv: 1804.00991

   2017
4. Valery Gritsenko, Viacheslav V. Nikulin, Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras, 2017 , 15 pp., arXiv: 1702.07551
5. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. III”, Izv. Math., 81:5 (2017), 985–1029  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
6. Viacheslav V. Nikulin, Classification of Picard lattices of K3 surfaces, 2017 , 68 pp., arXiv: 1707.05677
7. V. A. Gritsenko, V. V. Nikulin, “Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras”, Trans. Moscow Math. Soc., 78 (2017), 75–83  mathnet  crossref  scopus

   2016
8. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. II”, Izv. Math., 80:2 (2016), 359–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  elib  scopus (cited: 1)
9. Valery Gritsenko, Viacheslav V. Nikulin, Lorentzian Kac–Moody algebras with Weyl groups of 2-reflection, 2016 , 73 pp., arXiv: 1602.08359
10. Viacheslav V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices, II”, Adv. Stud. Pure Math., 69, 2016, 421–471  mathnet  isi (cited: 2)

   2015
11. V. V. Nikulin, Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, II, 2015 , 55 pp., arXiv: 1504.00326v4
12. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups”, Izv. Math., 79:4 (2015), 740–794  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
13. V. V. Nikulin, “Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups.”, Conference on K3 surfaces and related topics (KIAS, Seoul, Korea, 16–20 November), 2015 , 1 pp. http://home.kias.re.kr/MKG/h/K3surfaces/  mathscinet (cited: 2)

   2014
14. V. V. Nikulin, “Elliptic fibrations on K3 surfaces”, Proc. Edinb. Math. Soc. (2), 57:1 (2014), 253–267  mathnet  crossref  mathscinet (cited: 1)  zmath  isi (cited: 1)  scopus (cited: 1)
15. V. V. Nikulin, Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, 2014 , 70 pp., arXiv: 1403.6061v3
16. V. V. Nikulin, “Kahlerian K3 surfaces and Niemeier lattices”, Workshop: Automorphic forms, Lie algebras and String theory (Lille University II, March 3–6), Lille, France, 2014 , 28 pp. http://www.ihes.fr/~vanhove/Lille2014/index.html
17. V. V. Nikulin, “Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups”, Conference: Moduli spaces of real and complex varieties (Angers University, June 2–6), Angers, France, 2014 , 1 pp. http://www.math.univ-angers.fr/~mangolte/Angers-2014-abstracts.pdf

   2013
18. V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. I”, Izv. Math., 77:5 (2013), 954–997  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 10)  elib  scopus (cited: 7)
19. V. V. Nikulin, “Kahlerian K3 surfaces and Niemeier lattices”, The 6th MSJ-SI-Development of Moduli Theory, Conference dedicated to 60th birthday of Mukai (Kyoto, RIMS, 17–21 June 2013), Research Institute of Mathematical Sciences (RIMS), Kyoto University, Japan, 2013, 1  mathscinet (cited: 1)
20. V. V. Nikulin, “Kahlerian K3 surfaces and Niemeier lattices”, Project: Mock modular forms, Moonshine and String Theory, 2013 (New York State, USA, 25 September 2013), Simons Center for Geomery and Physics, Stony Brook University, 2013, 1–1
21. F. A. Bogomolov, F. Kataneze, Yu. I. Manin, S. Yu. Nemirovskii, V. V. Nikulin, A. N. Parshin, V. V. Przhiyalkovskii, Yu. G. Prokhorov, M. Teikher, A. S. Tikhomirov, V. M. Kharlamov, I. A. Cheltsov, I. R. Shafarevich, V. V. Shokurov, “Viktor Stepanovich Kulikov (k shestidesyatiletiyu so dnya rozhdeniya)”, UMN, 68:2(410) (2013), 205–207  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib

   2011
22. V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. Math., 75:5 (2011), 971–1005  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)
23. Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib

   2010
24. F. A. Bogomolov, Yu. G. Zarhin, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, M. Reid, I. A. Cheltsov, “Vyacheslav Vladimirovich Shokurov (on his 60th birthday)”, Russian Math. Surveys, 65:6 (2010), 1193–1198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib

   2009
25. V. V. Nikulin, “On ground fields of arithmetic hyperbolic reflection groups”, Groups and symmetries, CRM Proc. Lecture Notes, 47, Amer. Math. Soc., Providence, RI, 2009, 299–326  crossref  mathscinet (cited: 6)  zmath  isi (cited: 3)
26. V. V. Nikulin, “On ground fields of arithmetic hyperbolic reflection groups. III”, J. Lond. Math. Soc. (2), 79:3 (2009), 738–756  crossref  mathscinet (cited: 5)  zmath  isi (cited: 3)  scopus (cited: 2)
27. V. V. Nikulin, “Self-correspondences of $K3$ surfaces via moduli of sheaves”, Algebra, arithmetic, and geometry, in honor of Yu. I. Manin, Vol. II, Progr. Math., 270, Birkhäuser Boston Inc., Boston, MA, 2009, 439–464  mathscinet (cited: 2)  zmath  adsnasa
28. F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

   2008
29. V. V. Nikulin, Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups, 2008 , arXiv: 0810.2945  adsnasa
30. V. V. Nikulin, “On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II”, Mosc. Math. J., 8:4 (2008), 789–812  mathnet (cited: 3)  mathscinet (cited: 3)  zmath  isi (cited: 3)
31. C. G. Madonna, V. V. Nikulin, “Explicit correspondences of a K3 surface with itself”, Izv. Math., 72:3 (2008), 497–508  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)
32. V. V. Nikulin, “On the connected components of moduli of real polarized $\mathrm K3$-surfaces”, Izv. Math., 72:1 (2008), 91–111  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  elib  scopus (cited: 2)

   2007
33. V. V. Nikulin, S. Saito, “Real $K3$ surfaces with non-symplectic involution and applications. II”, Proc. Lond. Math. Soc. (3), 95:1 (2007), 20–48  crossref  mathscinet (cited: 1)  zmath  isi  scopus (cited: 1)
34. V. V. Nikulin, “On correspondences of a $K3$ surface with itself. II”, Algebraic geometry, Contemp. Math., 422, Amer. Math. Soc., Providence, RI, 2007, 121–172  crossref  mathscinet (cited: 3)  zmath  isi (cited: 3)
35. V. V. Nikulin, “Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces”, Izv. Math., 71:1 (2007), 53–56  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 15)  elib  scopus (cited: 4)

   2006
36. V. Alexeev, V. V. Nikulin, Del Pezzo and $K3$ surfaces, MSJ Memoirs, 15, Mathematical Society of Japan, Tokyo, 2006 , xvi+149 pp.  mathscinet (cited: 45)  zmath

   2005
37. V. V. Nikulin, S. Saito, “Real $K3$ surfaces with non-symplectic involution and applications”, Proc. London Math. Soc. (3), 90:3 (2005), 591–654  crossref  mathscinet (cited: 6)  zmath  isi (cited: 6)  scopus (cited: 6)

   2004
38. V. V. Nikulin, “On algebraic varieties with finite polyhedral Mori cone”, The Fano Conference, Univ. Torino, Turin, 2004, 573–589  mathscinet (cited: 1)  zmath
39. C. Madonna, V. V. Nikulin, “On a classical correspondence between $K3$ surfaces. II”, Strings and geometry, Clay Math. Proc., 3, Amer. Math. Soc., Providence, RI, 2004, 285–300  mathscinet (cited: 6)  zmath
40. V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226  mathnet  mathscinet  zmath

   2003
41. C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153  mathnet  mathscinet  zmath
42. F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi

   2002
43. V. A. Gritsenko, V. V. Nikulin, “On classification of Lorentzian Kac–Moody algebras”, Russian Math. Surveys, 57:5 (2002), 921–979  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 19)  elib (cited: 12)  scopus (cited: 16)

   1996
44. V. V. Nikulin, “A remark on discriminants of moduli of $K3$ surfaces as sets of zeros of automorphic forms”, J. Math. Sci., 81:3 (1996), 2738–2743  mathnet  crossref  mathscinet  zmath  scopus (cited: 12)

   2000
45. V. V. Nikulin, “A remark on algebraic surfaces with polyhedral Mori cone”, Nagoya Math. J., 157 (2000), 73–92  crossref  mathscinet (cited: 8)  zmath  isi (cited: 8)  scopus (cited: 9)
46. V. A. Gritsenko, V. V. Nikulin, “The arithmetic mirror symmetry and Calabi-Yau manifolds”, Comm. Math. Phys., 210:1 (2000), 1–11  crossref  mathscinet (cited: 14)  zmath  adsnasa  isi (cited: 7)  scopus (cited: 10)
47. V. V. Nikulin, “On the Classification of Hyperbolic Root Systems of Rank Three”, Proc. Steklov Inst. Math., 230:3 (2000), 1–241  mathnet  mathscinet  zmath  zmath

   1999
48. V. V. Nikulin, “$K3$ surfaces with interesting groups of automorphisms”, Algebraic geometry, 8, J. Math. Sci. (New York), 95:1 (1999), 2028–2048  crossref  mathscinet (cited: 8)  zmath  scopus (cited: 7)

   2001
49. V. V. Nikulin, “A theory of Lorentzian Kac–Moody algebras”, J. Math. Sci. (New York), 106:4 (2001), 3212–3221  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)

   1999
50. A. I. Kostrikin, V. S. Kulikov, Yu. I. Manin, V. V. Nikulin, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, A. N. Tyurin, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (on his 60th birthday)”, Russian Math. Surveys, 54:4 (1999), 863–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi

   1998
51. V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. II”, Internat. J. Math., 9:2 (1998), 201–275  crossref  mathscinet (cited: 53)  zmath  isi (cited: 59)
52. V. A. Gritsenko, V. V. Nikulin, “Automorphic forms and Lorentzian Kac-Moody algebras. I”, Internat. J. Math., 9:2 (1998), 153–199  crossref  mathscinet (cited: 23)  zmath  isi (cited: 30)

   1997
53. V. A. Gritsenko, V. V. Nikulin, “Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras”, Amer. J. Math., 119:1 (1997), 181–224  crossref  mathscinet (cited: 46)  zmath  isi (cited: 62)  scopus (cited: 61)

   1996
54. V. V. Nikulin, “The diagram method for 3-folds and its application to the Kähler cone and Picard number of Calabi-Yau 3-folds. I”, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 261–328  mathscinet (cited: 12)  zmath  isi (cited: 2)
55. V. A. Gritsenko, V. V. Nikulin, “$K3$ surfaces, Lorentzian Kac-Moody algebras and mirror symmetry”, Math. Res. Lett., 3:2 (1996), 211–229  crossref  mathscinet (cited: 19)  zmath  scopus (cited: 19)
56. V. V. Nikulin, “On the topological classification of real Enriques surfaces. I”, Topology of real algebraic varieties and related topics, Amer. Math. Soc. Transl. Ser. 2, 173, Amer. Math. Soc., Providence, RI, 1996, 187–201  mathscinet (cited: 1)  zmath  isi (cited: 85)
57. V. V. Nikulin, “Basis of the diagram method for generalized reflection groups in Lobachevsky spaces and algebraic surfaces with nef anticanonical class”, Internat. J. Math., 7:1 (1996), 71–108  crossref  mathscinet (cited: 5)  zmath  isi (cited: 5)  scopus (cited: 7)
58. V. A. Gritsenko, V. V. Nikulin, “Igusa modular forms and 'the simplest' Lorentzian Kac–Moody algebras”, Sb. Math., 187:11 (1996), 1601–1641  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 22)  elib (cited: 20)  scopus (cited: 21)
59. V. V. Nikulin, “Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac–Moody algebras”, Izv. Math., 60:2 (1996), 305–334  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 10)  scopus (cited: 7)

   1995
60. V. A. Gritsenko, V. V. Nikulin, “Automorphic correction of a Lorentzian Kac-Moody algebra”, C. R. Acad. Sci. Paris Sér. I Math., 321:9 (1995), 1151–1156  mathscinet (cited: 8)  zmath  isi (cited: 13)

   1994
61. V. V. Nikulin, “On the Picard number of Fano 3-folds with terminal singularities”, J. Math. Kyoto Univ., 34:3 (1994), 495–529  crossref  mathscinet (cited: 1)  zmath  isi (cited: 2)
62. V. V. Nikulin, “On the Brauer group of real algebraic surfaces”, Algebraic geometry and its applications (Yaroslavl', 1992), Aspects Math., E25, Vieweg, Braunschweig, 1994, 113–136  crossref  mathscinet (cited: 8)  zmath  isi (cited: 8)

   1993
63. V. V. Nikulin, R. Sujatha, “On Brauer groups of real Enriques surfaces”, J. Reine Angew. Math., 444 (1993), 115–154  crossref  mathscinet (cited: 5)  zmath  isi (cited: 10)  scopus (cited: 8)

   1991
64. V. V. Nikulin, “Weil linear systems on singular $K3$ surfaces”, Algebraic geometry and analytic geometry (1990, Tokyo), ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, 138–164  crossref  mathscinet (cited: 11)  zmath
65. V. V. Nikulin, “On rational maps between $K3$ surfaces”, Constantin Carathéodory: an international tribute, v. II, World Sci. Publ., Teaneck, NJ, 1991, 964–995  crossref  mathscinet (cited: 6)  zmath
66. V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189  mathnet  crossref  mathscinet  zmath  adsnasa  scopus

   1989
67. V. A. Alekseev, V. V. Nikulin, “Classification of del Pezzo surfaces with log-terminal singularities of index $\le 2$, and involutions on K3 surfaces”, Soviet Math. Dokl., 39:3 (1989), 507–511  mathnet  mathscinet  zmath  isi (cited: 4)

   1990
68. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675  mathnet  crossref  mathscinet  zmath
69. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 3)

   1989
70. V. I. Arnol'd, O. Ya. Viro, E. A. Leontovich-Andronova, V. V. Nikulin, S. P. Novikov, O. A. Oleinik, G. M. Polotovsky, V. M. Kharlamov, “Dmitrii Andreevich Gudkov (on his seventieth birthday)”, Russian Math. Surveys, 44:1 (1989), 271–273  mathnet  crossref  mathscinet  adsnasa  isi

   1988
71. V. A. Alekseev, V. V. Nikulin, “Classification of del Pezzo surfaces with log-terminal singularities of index $\le 2$, involutions on $K3$ surfaces, and reflection groups in Lobachevskiĭ spaces”, Lectures in mathematics and its applications, 2, no. 2, Ross. Akad. Nauk, Inst. Mat. im. Steklova, Moscow; Tul'sk. Politekhn. Inst., Tula, 1988, 51–150  mathscinet

   1989
72. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)

   1987
73. V. V. Nikulin, “Discrete reflection groups in Lobachevsky spaces and algebraic surfaces”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, 2, Amer. Math. Soc., Providence, RI, 1987, 654–671  mathscinet (cited: 39)  zmath
74. V. V. Nikulin, I. R. Shafarevich, Geometries and groups, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987 , viii+251 pp.  mathscinet (cited: 5)  zmath

   1988
75. V. V. Nikulin, “On correspondences between K3 surfaces”, Math. USSR-Izv., 30:2 (1988), 375–383  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)

   1987
76. V. V. Nikulin, “Local invariants of 4-dimensional pseudo-Riemannian manifolds with a Lorentz metric”, J. Soviet Math., 37:4 (1987), 1210–1238  mathnet  crossref  mathscinet  zmath  scopus

   1986
77. V. V. Nikulin, “Filtrations of 2-elementary forms and involutions of integral symmetric and skew-symmetric bilinear forms”, Math. USSR-Izv., 27:1 (1986), 159–182  mathnet  crossref  mathscinet  zmath  scopus

   1984
78. V. V. Nikulin, “On a description of the automorphism groups of Enriques surfaces”, Sov. Math. Dokl., 30 (1984), 282–285  mathnet  mathscinet  zmath  isi (cited: 6)
79. V. V. Nikulin, “$K3$ surfaces with a finite group of automorphisms and a Picard group of rank three”, Algebraic geometry and its applications, Collection of articles, Trudy Mat. Inst. Steklov., 165, 1984, 119–142  mathnet  mathscinet  zmath

   1983
80. V. V. Nikulin, I. R. Shafarevich, Geometrii i gruppy, Nauka, M., 1983 , 240 pp.  mathscinet (cited: 1)  zmath

   1984
81. V. V. Nikulin, “Involutions of integral quadratic forms and their applications to real algebraic geometry”, Math. USSR-Izv., 22:1 (1984), 99–172  mathnet  crossref  mathscinet  zmath  scopus (cited: 8)

   1983
82. V. V. Nikulin, “Quotient-groups of groups of automorphisms of hyperbolic forms by subgroups generated by 2-reflections. Algebro-geometric applications”, J. Soviet Math., 22:4 (1983), 1401–1475  mathnet  crossref  mathscinet  zmath  scopus (cited: 79)

   1982
83. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 13)

   1981
84. V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Math. USSR-Izv., 16:3 (1981), 573–601  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 19)  scopus (cited: 15)

   1979
85. V. V. Nikulin, “Konechnye gruppy avtomorfizmov kelerovykh poverkhnostei tipa $K_3$”, Tr. MMO, 38, Izd-vo Mosk. un-ta, M., 1979, 75–137  mathnet (cited: 16)  mathscinet (cited: 135)  zmath
86. V. V. Nikulin, “On factor groups of the automorphism groups of hyperbolic forms modulo subgroups generated by 2-reflections”, Sov. Math. Dokl., 20 (1979), 1156–1158  mathscinet  zmath  isi

   1980
87. V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167  mathnet  crossref  mathscinet  zmath  isi (cited: 332)  scopus (cited: 271)

   1976
88. V. V. Nikulin, “Finite groups of automorphisms of Kählerian surfaces of type K3”, Uspekhi Mat. Nauk, 31:2(188) (1976), 223–224  mathnet  mathscinet  zmath

   1975
89. V. V. Nikulin, “On Kummer surfaces”, Math. USSR-Izv., 9:2 (1975), 261–275  mathnet  crossref  mathscinet  zmath  scopus (cited: 41)

   1974
90. V. V. Nikulin, “An analogue of the Torelli theorem for Kummer surfaces of Jacobians”, Math. USSR-Izv., 8:1 (1974), 21–41  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)

Presentations in Math-Net.Ru
1. Вырождения и решетки Пикара К3-поверхностей с конечными симплектическими группами автоморфизмов
V. V. Nikulin
Steklov Mathematical Institute Seminar
April 19, 2018 16:00   
2. Classification of Picard lattices of $K3$ surfaces
V. V. Nikulin
"Algebra, algebraic geometry, and number theory". Memorial conference for academician Igor Rostislavovich Shafarevich
June 5, 2017 15:50   
3. Arithmetic mirror symmetry for K3 surfaces.
V. V. Nikulin
Automorphic forms and their applications
January 17, 2017 18:00   
4. Lorentzian Kac-Moody algebras and automorphic forms. Introduction.
V. V. Nikulin
Automorphic forms and their applications
September 29, 2015 18:30   
5. Classfication of degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups, II
V. V. Nikulin
Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
June 23, 2015 13:30
6. Классификация вырождений кэлеровых К3-поверхностей с конечными симплектическими группами автоморфизмов
V. V. Nikulin
Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
January 20, 2015 15:00
7. Пучки эллиптических кривых и группы автоморфизмов поверхностей K3
V. V. Nikulin
International conference dedicated to the 90th anniversary of academician Igor Rostislavovich Shafarevich
June 4, 2013 10:30   
8. Kahlerian K3 surfaces and Niemeier lattices
V. V. Nikulin
International conference "KUL!FEST" dedicated to the 60th anniversary of Vik. S. Kulikov
December 5, 2012 16:00   
9. Поверхности дель Пеццо и К3 III
V. V. Nikulin
Summer mathematical school "Algebra and Geometry", 2012
July 31, 2012 09:30   
10. Поверхности дель Пеццо и К3 II
V. V. Nikulin
Summer mathematical school "Algebra and Geometry", 2012
July 29, 2012 14:30   
11. Поверхности дель Пеццо и К3 I
V. V. Nikulin
Summer mathematical school "Algebra and Geometry", 2012
July 26, 2012 11:30   
12. Kähler K3 surfaces and Niemeier lattices
V. V. Nikulin
One-day conference dedicated to the memory of V. A. Iskovskikh
December 29, 2011 12:30   
13. Константа переноса для арифметических гиперболических групп отражений
V. V. Nikulin
Seminar of the Department of Algebra
July 6, 2010 14:00
14. On self-correspondences of K3 surfaces via moduli of sheaves
V. V. Nikulin
International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh
June 30, 2009 16:30   
15. On classification of arithmetic groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
International Conference of Steklov Institute Members, working outside Russia
June 6, 2009 12:30   
16. Соответствия поверхности K3 с собой с помощью модулей пучков, и арифметические группы отражений
V. V. Nikulin
Seminar of the Department of Algebra
April 21, 2009 15:00
17. О явных соответствиях поверхности К3 с собой с помошью модулей пучков
V. V. Nikulin
Seminar of the Department of Algebra
July 8, 2008 15:00
18. О классификации арифметических групп, порожденных отражениями, в пространствах Лобачевского
V. V. Nikulin
Seminar of the Department of Algebra
October 30, 2007 15:00
19. Соответствия K3-поверхности с собой, с использованием вектора Мукаи общего вида
V. V. Nikulin
Seminar of the Department of Algebra
January 17, 2006

Books in Math-Net.Ru
  1. V. V. Nikulin, On the classification of hyperbolic root systems of rank three, Tr. Mat. Inst. Steklova, 230, ed. I. R. Shafarevich, E. F. Mishchenko, 2000, 256 с.
    http://mi.mathnet.ru/book243

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