General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Izv. RAN. Ser. Mat.:

Personal entry:
Save password
Forgotten password?

Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 1, Pages 111–177 (Mi izv1677)  

This article is cited in 168 scientific papers (total in 168 papers)

Integral symmetric bilinear forms and some of their applications

V. V. Nikulin

Abstract: We set up the technique of discriminant-forms, which allows us to transfer many results for unimodular symmetric bilinear forms to the nonunimodular case and is convenient in calculations. Further, these results are applied to Milnor's quadratic forms for singularities of holomorphic functions and also to algebraic geometry over the reals.
Bibliography: 57 titles.

Full text: PDF file (6998 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1980, 14:1, 103–167

Bibliographic databases:

UDC: 511+513.6
MSC: Primary 10C05; Secondary 14B05, 14J25
Received: 12.06.1978

Citation: V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Izv. Akad. Nauk SSSR Ser. Mat., 43:1 (1979), 111–177; Math. USSR-Izv., 14:1 (1980), 103–167

Citation in format AMSBIB
\by V.~V.~Nikulin
\paper Integral symmetric bilinear forms and some of their applications
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 1
\pages 111--177
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 1
\pages 103--167

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Finashin S. Kharlamov V., “Chirality of Real Non-Singular Cubic Fourfolds and Their Pure Deformation Classification”, Rev. Mat. Complut.  crossref  isi
    2. 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
    3. A. N. Tyurin, “A local invariant of a Riemannian manifold”, Math. USSR-Izv., 19:1 (1982), 125–149  mathnet  crossref  mathscinet  zmath
    4. V. M. Kharlamov, “Rigid isotopic classification of real planar curves of degree 5”, Funct. Anal. Appl., 15:1 (1981), 73–74  mathnet  crossref  mathscinet  zmath  isi
    5. T. Fidler, “Pencils of lines and the topology of real algebraic curves”, Math. USSR-Izv., 21:1 (1983), 161–170  mathnet  crossref  mathscinet  zmath
    6. V. A. Krasnov, “Harnack–Thom inequalities for mappings of real algebraic varieties”, Math. USSR-Izv., 22:2 (1984), 247–275  mathnet  crossref  mathscinet  zmath
    7. M. Sh. Farber, “The classification of simple knots”, Russian Math. Surveys, 38:5 (1983), 63–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. 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
    9. V. M. Kharlamov, “Classification of nonsingular surfaces of degree $4$ in $\mathbb{RP}^3$ with respect to rigid isotopies”, Funct. Anal. Appl., 18:1 (1984), 39–45  mathnet  crossref  mathscinet  zmath  isi
    10. 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
    11. O. Ya. Viro, “Progress in the topology of real algebraic varieties over the last six years”, Russian Math. Surveys, 41:3 (1986), 55–82  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. G. M. Polotovsky, “Connection between the rigid isotopy class of a fifth-order nonsingular curve in $\mathbb{R}P^2$ and its disposition with respect to a line”, Funct. Anal. Appl., 20:4 (1986), 330–332  mathnet  crossref  mathscinet  zmath  isi
    13. Eduard Looijenga, Jonathan Wahl, “Quadratic functions and smoothing surface singularities”, Topology, 25:3 (1986), 261  crossref
    14. V. V. Nikulin, “On correspondences between K3 surfaces”, Math. USSR-Izv., 30:2 (1988), 375–383  mathnet  crossref  mathscinet  zmath
    15. Shigeyuki Kondō, “On the Albanese variety of the moduli space of polarizedK3 surfaces”, Invent math, 91:3 (1988), 587  crossref  mathscinet  zmath  isi
    16. Rick Miranda, “Persson's list of singular fibers for a rational elliptic surface”, Math Z, 205:1 (1990), 191  crossref  mathscinet  zmath  isi
    17. Brian Harbourne, Rick Miranda, “Exceptional curves on rational numerically elliptic surfaces”, Journal of Algebra, 128:2 (1990), 405  crossref
    18. Hans Sterk, “Compactifications of the period space of Enriques surfaces Part I”, Math Z, 207:1 (1991), 1  crossref  mathscinet  zmath  isi
    19. V. A. Krasnov, “Algebraic cycles on a real algebraic GM-manifold and their applications”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 141–160  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. Jürg Fröhlich, Emmanuel Thiran, “Integral quadratic forms, Kac-Moody algebras, and fractional quantum Hall effect. AnADE-O classification”, J Statist Phys, 76:1-2 (1994), 209  crossref  mathscinet  adsnasa
    21. Donald G. James, “Representations by unimodular quadratic ℤ-lattices”, Math Z, 215:1 (1994), 465  crossref  mathscinet  zmath  isi
    22. Rudolf Scharlau, Boris B. Venkov, “The genus of the Barnes-Wall lattice”, Comment Math Helv, 69:1 (1994), 322  crossref  mathscinet  zmath  isi  elib
    23. Hans Sterk, “Lattices and K3 surfaces of degree 6”, Linear Algebra and its Applications, 226-228 (1995), 297  crossref
    24. 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  elib
    25. D. O. Orlov, “Equivalences of derived categories andK3 surfaces”, Journal of Mathematical Sciences (New York), 84:5 (1997), 1361  crossref  mathscinet  zmath
    26. Ori J. Ganor, David R. Morrison, Nathan Seiberg, “Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory”, Nuclear Physics B, 487:1-2 (1997), 93  crossref
    27. Gritsenko V.A., Nikulin V.V., “Automorphic forms and Lorentzian Kac-Moody algebras. Part I”, International Journal of Mathematics, 9:2 (1998), 153–199  crossref  mathscinet  zmath  isi  elib
    28. Gritsenko V.A., Nikulin V.V., “Automorphic forms and Lorentzian Kac-Moody algebras. Part II”, International Journal of Mathematics, 9:2 (1998), 201–275  crossref  mathscinet  zmath  isi  elib
    29. Andrei Mikhailov, “Momentum lattice for CHL string”, Nuclear Physics B, 534:3 (1998), 612  crossref
    30. A. I. Degtyarev, V. I. Zvonilov, “Rigid isotopy classification of real algebraic curves of bidegree $(3,3)$ on quadrics”, Math. Notes, 66:6 (1999), 670–674  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. V. G. Zhuravlev, “Embedding $p$-elementary lattices”, Izv. Math., 63:1 (1999), 73–102  mathnet  crossref  crossref  mathscinet  zmath  isi
    32. V. A. Krasnov, “Real algebraic varieties without real points”, Izv. Math., 63:4 (1999), 757–790  mathnet  crossref  crossref  mathscinet  zmath  isi
    33. Robbert Dijkgraaf, “Instanton strings and hyper-Kähler geometry”, Nuclear Physics B, 543:3 (1999), 545  crossref
    34. 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
    35. Degtyarev A., Itenberg I., Kharlamov V., Real Enriques surfaces, Lecture Notes in Math., 1746, Springer-Verlag, Berlin, 2000, xvi+259 pp.  crossref  mathscinet  zmath  isi
    36. Gritsenko V.A., Nikulin V.V., “The arithmetic mirror symmetry and Calabi-Yau manifolds”, Communications in Mathematical Physics, 210:1 (2000), 1–11  crossref  mathscinet  zmath  adsnasa  isi  elib
    37. Eberhard Freitag, Carl Friedrich Hermann, “Some Modular Varieties of Low Dimension”, Advances in Mathematics, 152:2 (2000), 203  crossref
    38. Myung-Hwan Kim, Byeong-Kweon Oh, “Generation of Isometries of Certain -Lattices by Symmetries”, Journal of Number Theory, 83:1 (2000), 76  crossref
    39. Kondo S., “A Complex Hyperbolic Structure for the Moduli Space of Curves of Genus Three”, J. Reine Angew. Math., 525 (2000), 219–232  crossref  mathscinet  zmath  isi
    40. A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    42. 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  elib
    43. Degtyarev A., Kharlamov V., “Real rational surfaces are quasi-simple”, Journal fur Die Reine und Angewandte Mathematik, 551 (2002), 87–99  mathscinet  zmath  isi  elib
    44. Sarah-Marie Belcastro, “PICARD LATTICES OF FAMILIES OF K3 SURFACES”, Communications in Algebra, 30:1 (2002), 61  crossref
    45. J. Keum, D.-Q. Zhang, “Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds”, Journal of Pure and Applied Algebra, 170:1 (2002), 67  crossref
    46. Robert L. Griess, Gerald Höhn, “Virasoro frames and their stabilizers for the E<sub>8</sub> lattice type vertex operator algebra”, crll, 2003:561 (2003), 1  crossref
    47. C. G. Madonna, V. V. Nikulin, “On a Classical Correspondence between K3 Surfaces”, Proc. Steklov Inst. Math., 241 (2003), 120–153  mathnet  mathscinet  zmath
    48. D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    49. Trygve Johnsen, Andreas Leopold Knutsen, “Rational Curves in Calabi-Yau Threefolds”, Communications in Algebra, 31:8 (2003), 3917  crossref
    50. Catanese F. Frediani P., “Real Hyperelliptic Surfaces and the Orbifold Fundamental Group”, J. Inst. Math. Jussieu, 2:2 (2003), 169–233  crossref  isi
    51. Shinobu Hosono, B.H.. Lian, Keiji Oguiso, Shing-Tung Yau, “c = 2 Rational Toroidal Conformal Field Theories via the Gauss Product”, Commun. Math. Phys, 241:2-3 (2003), 245  crossref
    52. Paolo Stellari, “Some Remarks about the FM-partners of K3 Surfaces with Picard Numbers 1 and 2”, Geom Dedicata, 108:1 (2004), 1  crossref  mathscinet  zmath
    53. V. V. Nikulin, “On Correspondences of a K3 Surface with Itself. I”, Proc. Steklov Inst. Math., 246 (2004), 204–226  mathnet  mathscinet  zmath
    54. Degtyarev A., Itenberg I., Kharlamov V., “Finiteness and quasi-simplicity for symmetric K3-surfaces”, Duke Mathematical Journal, 122:1 (2004), 1–49  crossref  mathscinet  zmath  isi
    55. Nils R. Scheithauer, “Generalized Kac–Moody algebras, automorphic forms and Conway's group I”, Advances in Mathematics, 183:2 (2004), 240  crossref
    56. Daniel Huybrechts, Paolo Stellari, “Equivalences of twisted K3 surfaces”, Math Ann, 332:4 (2005), 901  crossref  mathscinet  zmath  isi  elib
    57. Bert van Geemen, “Some remarks on Brauer groups of K3 surfaces”, Advances in Mathematics, 197:1 (2005), 222  crossref
    59. Shigeyuki Kondō, “Maximal subgroups of the Mathieu group M23 and symplectic automorphisms of supersingular K3 surfaces”, Internat Math Res Notices, 2006 (2006), 1  crossref  zmath
    60. Vik. S. Kulikov, V. M. Kharlamov, “Surfaces with DIF$\ne$DEF real structures”, Izv. Math., 70:4 (2006), 769–807  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    61. D.-Q. Zhang, “The alternating groups and K3 surfaces”, Journal of Pure and Applied Algebra, 207:1 (2006), 119  crossref
    62. Kharlamov V., “Overview of topological properties of real algebraic surfaces”, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization, 2006, 103–117  isi
    63. Paolo Stellari, “Derived categories and Kummer varieties”, Math Z, 256:2 (2007), 425  crossref  mathscinet  zmath  isi  elib
    64. Frédéric Bihan, Frédéric Mangolte, “Topological types of real regular Jacobian elliptic surfaces”, Geom Dedicata, 127:1 (2007), 57  crossref  mathscinet  isi  elib
    65. Ken-Ichi Yoshikawa, “Real K3 surfaces without real points, equivariant determinant of the Laplacian, and the Borcherds Φ-function”, Math Z, 258:1 (2007), 213  crossref  mathscinet  isi
    66. Antonio Rapagnetta, “On the Beauville form of the known irreducible symplectic varieties”, Math Ann, 340:1 (2007), 77  crossref  mathscinet  zmath  isi
    67. V. A. Krasnov, “Fano Surfaces of Real Quartics”, Math. Notes, 81:1 (2007), 72–84  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    68. A. I. Degtyarev, I. V. Itenberg, V. M. Kharlamov, “Deformation finiteness for real hyperkähler manifolds”, Mosc. Math. J., 7:2 (2007), 257–263  mathnet  crossref  mathscinet  zmath
    69. Adrian Clingher, Charles F. Doran, “On K3 surfaces with large complex structure”, Advances in Mathematics, 215:2 (2007), 504  crossref
    70. V. V. Nikulin, “On the connected components of moduli of real polarized K3-surfaces”, Izv. Math., 72:1 (2008), 91–111  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    71. Shamik Banerjee, Ashoke Sen, “Duality orbits, dyon spectrum and gauge theory limit of heterotic string theory on T<sup>6</sup>”, J High Energy Phys, 2008:3 (2008), 022  crossref  mathscinet
    72. Alessandra Sarti, “Transcendental lattices of someK 3-surfaces”, Math Nachr, 281:7 (2008), 1031  crossref  mathscinet  zmath  isi
    73. Michela Artebani, Alessandra Sarti, “Non-symplectic automorphisms of order 3 on K3 surfaces”, Math Ann, 342:4 (2008), 903  crossref  mathscinet  zmath  isi
    74. Finashin S., Kharlamov V., “Deformation classes of real four-dimensional cubic hypersurfaces”, J. Algebraic Geom., 17:4 (2008), 677–707  mathscinet  zmath  isi  elib
    75. Degtyarev A., Itenberg I., Kharlamov V., “On deformation types of real elliptic surfaces”, Amer. J. Math., 130:6 (2008), 1561–1627  crossref  mathscinet  zmath  isi  elib
    76. Macri E., Stellari P., “Automorphisms and autoequivalences of generic analytic K3 surfaces”, Journal of Geometry and Physics, 58:1 (2008), 133–164  crossref  mathscinet  zmath  adsnasa  isi
    77. Markman E., “On the monodromy of moduli spaces of sheaves on K3 surfaces”, Journal of Algebraic Geometry, 17:1 (2008), 29–99  mathscinet  isi  elib
    79. V. A. Krasnov, “On the Fano Variety of a Class of Real Four-Dimensional Cubics”, Math. Notes, 85:5 (2009), 682–689  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    80. Schütt M., “CM newforms with rational coefficients”, Ramanujan J., 19:2 (2009), 187–205  crossref  mathscinet  zmath  isi
    81. Macri E., Stellari P., “Infinitesimal Derived Torelli Theorem for K3 Surfaces (with an Appendix by Sukhendu Mehrotra)”, Internat Math Res Notices, 2009, no. 17, 3190  crossref  mathscinet  zmath  isi
    82. Vijay Kumar, Washington Taylor, “Freedom and constraints in the K3 landscape”, J High Energy Phys, 2009:5 (2009), 066  crossref  mathscinet  adsnasa  isi
    83. Finashin, S, “On the deformation chirality of real cubic fourfolds”, Compositio Mathematica, 145:5 (2009), 1277  crossref  mathscinet  zmath  isi
    84. Huybrechts D., “The Global Torelli Theorem: classical, derived, twisted”, Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 80, no. 1- 2, 2009, 235–258  isi
    85. V. A. Krasnov, “Equivariant Topological Classification of the Fano Varieties of Real Four-Dimensional Cubics”, Math. Notes, 85:4 (2009), 574–583  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    86. Artebani M., Sarti A., Taki Sh., “$K3$ surfaces with non-symplectic automorphisms of prime order”, Math. Z., 2010  crossref
    87. Hulek K., Schütt M., “Enriques surfaces and Jacobian elliptic K3 surfaces”, Math. Z., 2010  crossref
    88. Finashin S., Kharlamov V., “Topology of real cubic fourfolds”, Journal of Topology, 3:1 (2010), 1–28  crossref  mathscinet  isi
    89. Radu Laza, “The moduli space of cubic fourfolds via the period map”, Ann of Math, 172:1 (2010), 673  crossref  mathscinet
    90. S. Kondo, “Moduli of Plane Quartics, Gopel Invariants and Borcherds Products”, Internat Math Res Notices, 2010  crossref
    91. Shingo Taki, “Classification of non-symplectic automorphisms of order 3 on K3 surfaces”, Math. Nachr, 2010, n/a  crossref
    92. Allcock D., Carlson J.A., Toledo D., “Hyperbolic Geometry and Moduli of Real Cubic Surfaces”, Annales Scientifiques de l Ecole Normale Superieure, 43:1 (2010), 69–115  mathscinet  isi
    93. Kenji Hashimoto, Tomohide Terasoma, “Period map of a certainK3 family with an 𝔖5-action”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2010, -  crossref
    94. Diarmuid Crowley, Jörg Sixt, “Stably diffeomorphic manifolds andl2q+1(ℤ[π])”, Forum Mathematicum, 2010, -  crossref
    95. Matthias Schütt, “K3 surfaces with non-symplectic automorphisms of 2-power order”, Journal of Algebra, 323:1 (2010), 206  crossref
    96. Ron Livné, Matthias Schütt, Noriko Yui, “The modularity of K3 surfaces with non-symplectic group actions”, Math. Ann, 348:2 (2010), 333  crossref
    97. Jin-Gen Yang, Jinjing Xie, “Discrminantal groups and Zariski pairs of sextic curves”, Geom Dedicata, 2011  crossref
    98. Ursula Whitcher, “Symplectic Automorphisms and the Picard Group of a K3 Surface”, Comm. in Algebra, 39:4 (2011), 1427  crossref
    99. Ken-Ichi Yoshikawa, “K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space III: the case r(M) ≥ 18”, Math. Z, 2011  crossref
    100. Frederik Denef, Gregory W. Moore, “Split states, entropy enigmas, holes and halos”, J. High Energ. Phys, 2011:11 (2011)  crossref
    101. Toshiyuki Katsura, Shigeyuki Kondō, “Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3”, Journal of Algebra, 2011  crossref
    102. Kenji Koike, “Hessian K3 surfaces of non-Sylvester type”, Journal of Algebra, 330:1 (2011), 388  crossref
    103. Degtyarev A., “Topology of plane algebraic curves: the algebraic approach”, Topology of Algebraic Varieties and Singularities, Contemporary Mathematics, 538, 2011, 137–161  crossref  isi
    104. Anton Kapustin, Natalia Saulina, “Topological boundary conditions in abelian Chern–Simons theory”, Nuclear Physics B, 845:3 (2011), 393  crossref
    105. Artebani M. Kondo Sh., “The Moduli of Curves of Genus Six and K3 Surfaces”, Trans. Am. Math. Soc., 363:3 (2011), 1445–1462  crossref  mathscinet  zmath  isi
    106. V. A. Krasnov, “Real Two-Dimensional Intersections of a Quadric by a Cubic”, Math. Notes, 90:4 (2011), 509–516  mathnet  crossref  crossref  mathscinet  isi
    107. 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  elib
    108. Emanuele Macrì, Paolo Stellari, “Fano varieties of cubic fourfolds containing a plane”, Math. Ann, 2012  crossref
    109. Mang Xu, JiaJin Zhang, “Lattices, Diophantine equations and applications to rational surfaces”, Sci. China Math, 2012  crossref
    110. Shingo Taki, “Classification of non-symplectic automorphisms on K3 surfaces which act trivially on the Néron–Severi lattice”, Journal of Algebra, 358 (2012), 16  crossref
    111. Shigeyuki Kondō, “The moduli space of Hessian quartic surfaces and automorphic forms”, Journal of Pure and Applied Algebra, 2012  crossref
    112. Kwang-Woo Lee, “WHICH K3 SURFACES WITH PICARD NUMBER 19 COVER AN ENRIQUES SURFACE”, Bulletin of the Korean Mathematical Society, 49:1 (2012), 213  crossref
    113. Giovanni Mongardi, “Symplectic involutions on deformations of K3[2]”, centr.eur.j.math, 10:4 (2012), 1472  crossref
    114. Adrian Clingher, Charles F. Doran, “Lattice polarized K3 surfaces and Siegel modular forms”, Advances in Mathematics, 231:1 (2012), 172  crossref
    115. Max Pumperla, Frank Reidegeld, “-manifolds from surfaces with non-symplectic automorphisms”, Journal of Geometry and Physics, 2012  crossref
    116. Klaus Hulek, Matthias Schütt, “Arithmetic of singular Enriques surfaces”, ANT, 6:2 (2012), 195  crossref
    117. Madonna C.G., “On Some Moduli Spaces of Bundles on K3 Surfaces, II”, Proc. Amer. Math. Soc., 140:10 (2012), 3397–3408  isi
    119. Noam D. Elkies, Matthias Schütt, “Modular forms and K3 surfaces”, Advances in Mathematics, 240 (2013), 106  crossref
    120. Izv. Math., 77:3 (2013), 509–524  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    121. Markman E., “Prime Exceptional Divisors on Holomorphic Symplectic Varieties and Monodromy Reflections”, Kyoto J. Math., 53:2, 2 (2013), 345–403  crossref  zmath  isi
    122. Ciro Ciliberto, A.L.eopold Knutsen, “On k-gonal loci in Severi varieties on general K3 surfaces and rational curves on hyperkähler manifolds”, Journal de Mathématiques Pures et Appliquées, 2013  crossref
    123. A. Taormina, K. Wendland, “The overarching finite symmetry group of Kummer surfaces in the Mathieu group M 24”, J. High Energ. Phys, 2013:8 (2013)  crossref
    124. V. V. Nikulin, “Kählerian K3 surfaces and Niemeier lattices. I”, Izv. Math., 77:5 (2013), 954–997  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    125. V.V.. Nikulin, “Elliptic Fibrations On K3 Surfaces”, Proceedings of the Edinburgh Mathematical Society, 2013, 1  crossref
    126. Boissiere S. Nieper-Wisskirchen M. Sarti A., “Smith Theory and Irreducible Holomorphic Symplectic Manifolds”, J. Topol., 6:2 (2013), 361–390  crossref  isi
    127. Goto Ya., Livne R., Yui N., “Automorphy of Calabi-Yau Threefolds of Borcea-Voisin Type Over Q”, Commun. Number Theory Phys., 7:4 (2013), 581–670  isi
    128. Grgoire Menet, “Duality for relative Prymians associated to K3 double covers of del Pezzo surfaces of degree 2”, Math. Z, 2014  crossref
    129. Gerald Höhn, N.R.. Scheithauer, “A generalized Kac–Moody algebra of rank 14”, Journal of Algebra, 404 (2014), 222  crossref
    130. Jennifer Cano, Meng Cheng, Michael Mulligan, Chetan Nayak, Eugeniu Plamadeala, “Bulk-edge correspondence in (2 + 1)-dimensional Abelian topological phases”, Phys. Rev. B, 89:11 (2014)  crossref
    131. Michela Artebani, Samuel Boissière, Alessandra Sarti, “The Berglund–Hübsch–Chiodo–Ruan mirror symmetry for K3 surfaces”, Journal de Mathématiques Pures et Appliquées, 2014  crossref
    132. A. P. Braun, Y. Kimura, T. Watari, “The Noether-Lefschetz problem and gauge-group-resolved landscapes: F-theory on K3 × K3 as a test case”, J. High Energ. Phys, 2014:4 (2014)  crossref
    133. Ljudmila Kamenova, Misha Verbitsky, “Families of Lagrangian fibrations on hyperkähler manifolds”, Advances in Mathematics, 260 (2014), 401  crossref
    134. Ichiro Shimada, De-Qi Zhang, “Dynkin diagrams of rank 20 on supersingular K3 surfaces”, Sci. China Math, 2014  crossref
    135. Florian Beye, “Chiral four-dimensional heterotic covariant lattices”, J. High Energ. Phys, 2014:11 (2014)  crossref
    136. Dylan Attwell-Duval, “On the number of cusps of orthogonal Shimura varieties”, Ann. Math. Québec, 2014  crossref
    137. Comparin P., Garbagnati A., “Van Geemen-Sarti Involutions and Elliptic Fibrations on K3 Surfaces Double Cover of P-2”, J. Math. Soc. Jpn., 66:2 (2014), 479–522  crossref  isi
    138. J.O.. Kleppe, J.C.. Ottem, “Components of the Hilbert scheme of space curves on low-degree smooth surfaces”, Int. J. Math, 2015, 1550017  crossref
    139. K.G.. O’Grady, “Periods of double EPW-sextics”, Math. Z, 2015  crossref
    140. C.T.. McMullen, “Automorphisms of projective K3 surfaces with minimum entropy”, Invent. math, 2015  crossref
    141. Yichao Zhang, “Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms”, Journal of Number Theory, 155 (2015), 139  crossref
    142. G. Mongardi, M. Wandel, “Induced automorphisms on irreducible symplectic manifolds”, Journal of the London Mathematical Society, 2015  crossref
    143. M.C.. N. Cheng, Sarah Harrison, “Umbral Moonshine and K3 Surfaces”, Commun. Math. Phys, 2015  crossref
    144. Viatcheslav Kharlamov, Rareş Răsdeaconu, “Counting Real Rational Curves onK3 Surfaces”, Int Math Res Notices, 2015:14 (2015), 5436  crossref
    145. 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  elib  elib
    146. Shaul Zemel, “A p-adic approach to the Weil representation of discriminant forms arising from even lattices”, Ann. Math. Québec, 39:1 (2015), 61  crossref
    147. Esnault H. Oguiso K., “Non-Liftability of Automorphism Groups of a K3 Surface in Positive Characteristic”, Math. Ann., 363:3-4 (2015), 1187–1206  crossref  isi
    148. Ma Sh. Ohashi H. Taki Sh., “Rationality of the Moduli Spaces of Eisenstein K3 Surfaces”, Trans. Am. Math. Soc., 367:12 (2015), 8643–8679  crossref  isi
    149. Finashin S., Kharlamov V., “Apparent Contours of Nonsingular Real Cubic Surfaces”, Trans. Am. Math. Soc., 367:10 (2015), PII S0002-9947(2015)06286-2, 7221–7289  isi
    150. Ma Sh., “Rationality of the Moduli Spaces of 2-Elementary K3 Surfaces”, J. Algebr. Geom., 24:1 (2015), 81–158  isi
    151. 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  elib  elib
    152. Nikulin V.V., “Kahlerian K3 Surfaces and Niemeier Lattices, II”, Development of Moduli Theory - Kyoto 2013, Advanced Studies in Pure Mathematics, 69, ed. Fujino O. Kondo S. Moriwaki A. Saito M. Yoshioka K., Math Soc Japan, 2016, 421–471  mathscinet  isi
    153. Garbagnati A. Sarti A., “Kummer surfaces and K3 surfaces with $(\mathbb{Z} /2\mathbb{Z} )^4$ symplectic action”, Rocky Mt. J. Math., 46:4 (2016), 1141–1205  crossref  mathscinet  zmath  isi  scopus
    154. 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  elib
    155. Valery Gritsenko, Viacheslav 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  mathscinet  elib
    156. V. A. Krasnov, “On intersections of two real quadrics”, Izv. Math., 82:1 (2018), 91–139  mathnet  crossref  crossref  adsnasa  isi  elib
    157. Cheng M.C.N., Harrison S.M., Volpato R., Zimet M., “K3 String Theory, Lattices and Moonshine”, Res. Math. Sci., 5 (2018), 32  crossref  isi
    158. Rams S., Schuett M., “On Enriques Surfaces With Four Cusps”, Publ. Res. Inst. Math. Sci., 54:3 (2018), 433–468  crossref  isi
    159. V. A. Krasnov, “On a classical correspondence of real K3 surfaces”, Izv. Math., 82:4 (2018), 662–693  mathnet  crossref  crossref  adsnasa  isi  elib
    160. V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. Math., 82:4 (2018), 752–816  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    161. V. A. Gritsenko, “Reflective modular forms and applications”, Russian Math. Surveys, 73:5 (2018), 797–864  mathnet  crossref  crossref  adsnasa  isi  elib
    162. È. B. Vinberg, “On Some Free Algebras of Automorphic Forms”, Funct. Anal. Appl., 52:4 (2018), 270–289  mathnet  crossref  crossref  isi  elib
    163. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    164. Schaffler L., “K3 Surfaces With Z(2)(2) Symplectic Action”, Rocky Mt. J. Math., 48:7 (2018), 2347–2383  crossref  mathscinet  zmath  isi  scopus
    165. V. A. Krasnov, “Real Kummer surfaces”, Izv. Math., 83:1 (2019), 65–103  mathnet  crossref  crossref  adsnasa  isi  elib
    166. V. V. Nikulin, “Classification of degenerations and Picard lattices of Kählerian K3 surfaces with symplectic automorphism group $D_6$”, Izv. Math., 83:6 (2019), 1201–1233  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    167. V. A. Gritsenko, H. Wang, “Antisymmetric paramodular forms of weight 3”, Sb. Math., 210:12 (2019), 1702–1723  mathnet  crossref  crossref  isi  elib
    168. Viacheslav V. Nikulin, “Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group $C_4$”, Proc. Steklov Inst. Math., 307 (2019), 130–161  mathnet  crossref  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:2685
    Full text:978
    First page:2

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021