Persons: Pukhlikov, Aleksandr Valentinovich

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Pukhlikov, Aleksandr Valentinovich

Statistics
in MathSciNet:	103 (101)
in zbMATH:	94 (92)
in Web of Science:	70 (68)
in Scopus:	75 (75)

Doctor of physico-mathematical sciences (1998)

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

Birth date:

18.12.1962

E-mail:

Website:

https://www.liverpool.ac.uk/mathematical-sciences/staff/aleksandr-pukhlikov/

Keywords:

algebraic variety, Fano variety, Fano fibration, birational map, birational rigidity, divisor, linear system, singularity, intersection theory, optimal control, optimal system, discontinuous Hamiltonian system.

UDC:

512.76, 512.776, 512.724, 517.977, 513.6, 512.7, 519.6, 517.938

MSC:

14E05, 14E07, 14E08, 14J45, 14J30, 14M10, 14M20, 14M25, 14D06, 93C10, 37D40, 90C15, 34H05, 34D05, 93D05, 49K15

Subject:

Birational geometry of higher-dimensional algebraic varieties.

Biography

Graduated from Lomonosov Moscow State University (Department of Mathematics and Mechanics, Chair of Algebra) in 1984. Ph.D. (Cand. Sci.) — 1987 from Moscow State University. D.Sci. (Mathematics) — 1998 from Steklov Institute of Mathematics. The lists of my publications contains about 80 items. In 1998 I was an invited speaker at the International Congress of Mathematicians in Berlin (45-minute sectional address).

Main publications:

A. Pukhlikov, Birationally Rigid Varieties, Mathematical Surveys and Monographs, 190, Amer. Math. Soc., Providence, RI, 2013 , 367 pp.
A. V. Pukhlikov, “Birationally rigid Fano fibrations”, Izv. Math., 64:3 (2000), 563–581
A. V. Pukhlikov, “Birationally rigid Fano double hypersurfaces”, Sb. Math., 191:6 (2000), 883–908
A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces”, Invent. Math., 134:2 (1998), 401–426
A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155

https://www.mathnet.ru/eng/person8590

List of publications on Google Scholar

https://zbmath.org/authors/ai:pukhlikov.aleksandr-v

https://mathscinet.ams.org/mathscinet/MRAuthorID/231949

https://elibrary.ru/author_items.asp?authorid=4808

https://www.researchgate.net/profile/Aleksandr_Pukhlikov

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

Articles

1.	A. V. Pukhlikov, “Affine Complements in the Projective Space with Trivial Automorphism Group”, Proc. Steklov Inst. Math., 329 (2025), 207–216
2.	A. V. Pukhlikov, “Birationally rigid hypersurfaces with quadratic singularities of low rank”, Sb. Math., 215:6 (2024), 823–840
3.	A. V. Pukhlikov, “Birational geometry of varieties fibred into complete intersections of codimension two”, Izv. Math., 86:2 (2022), 334–411
4.	A. V. Pukhlikov, “Effective results in the theory of birational rigidity”, Russian Math. Surveys, 77:2 (2022), 301–354
5.	A. V. Pukhlikov, “Birational geometry of singular Fano double spaces of index two”, Sb. Math., 212:4 (2021), 551–566
6.	A. V. Pukhlikov, “Remarks on Galois Rational Coverings”, Math. Notes, 110:2 (2021), 242–247
7.	D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of high codimension”, Izv. Math., 83:4 (2019), 743–769
8.	A. V. Pukhlikov, “Birationally Rigid Finite Covers of the Projective Space”, Proc. Steklov Inst. Math., 307 (2019), 232–244
9.	A. V. Pukhlikov, “Automorphisms of certain affine complements in projective space”, Sb. Math., 209:2 (2018), 276–289
10.	Aleksandr V. Pukhlikov, “Canonical and log canonical thresholds of Fano complete intersections”, Eur. J. Math., 4:1 (2018), 381–398	5 ^[x]
11.	A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81:3 (2017), 618–644
12.	A. V. Pukhlikov, “Factorial hypersurfaces”, Proc. Steklov Inst. Math., 299 (2017), 205–218
13.	A. V. Pukhlikov, “The $4n^2$-inequality for complete intersection singularities”, Arnold Math. J., 3:2 (2017), 187–196	15 ^[x]
14.	D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of codimension two”, Bull. Korean Math. Soc., 54:5 (2017), 1627–1654
15.	Thomas Eckl, Aleksandr Pukhlikov, “On the global log canonical threshold of Fano complete intersections”, Eur. J. Math., 2:1 (2016), 291–303	5 ^[x]
16.	Aleksandr V. Pukhlikov, “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1 (2016), 721–782	11 ^[x]
17.	Aleksandr V. Pukhlikov, “The Gabrielov-Khovanskii problem for polynomials”, Arnold Math. J., 2:1 (2016), 29–68
18.	A. V. Pukhlikov, “Two Inequalities for a Sequence of Blow-Ups”, Math. Notes, 97:6 (2015), 970–973
19.	A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837
20.	Th. Eckl, A. Pukhlikov, “On the locus of nonrigid hypersurfaces”, Automorphisms in Birational and Affine Geometry (Levico Terme, Italy, October 2012), Springer Proceedings in Mathematics & Statistics, 79, Springer, 2014, 121–139	14 ^[x]
21.	A. V. Pukhlikov, “Birational Geometry of Higher-Dimensional Fano Varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150
22.	A. V. Pukhlikov, “Birationally rigid Fano complete intersections. II”, J. Reine Angew. Math., 2014:688 (2014), 209–218	7 ^[x]
23.	A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845
24.	A. V. Pukhlikov, “Birational rigidity of Fano complete intersections”, Dokl. Math., 87:1 (2013), 34–35
25.	A. V. Pukhlikov, “$K$-Trivial Structures on Fano Complete Intersections”, Math. Notes, 91:4 (2012), 568–574
26.	A. V. Pukhlikov, “On the multiplicity of solutions of a system of algebraic equations”, Proc. Steklov Inst. Math., 276 (2012), 234–249
27.	A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991
28.	A. V. Pukhlikov, “Existence of the Kähler–Einstein Metric on Certain Fano Complete Intersections”, Math. Notes, 88:4 (2010), 552–558
29.	A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171
30.	A. V. Pukhlikov, “Rationality problem and birational rigidity”, Cohomological and geometric approaches to rationality problems, Progr. Math., 282, Birkhäuser, Boston, 2009, 275–311
31.	A. V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano cyclic covers”, Pure Appl. Math. Q., 5:2, Special Issue: In honor of Friedrich Herzebruch (2009), 641–700	14 ^[x]
32.	A. V. Pukhlikov, “Singularities of Algebraic Subvarieties and Problems of Birational Geometry”, Proc. Steklov Inst. Math., 267 (2009), 235–247
33.	A. V. Pukhlikov, “Birational Geometry of Singular Fano Varieties”, Proc. Steklov Inst. Math., 264 (2009), 159–177
34.	A. V. Pukhlikov, “On the self-intersection of a movable linear system”, J. Math. Sci., 164:1 (2010), 119–130
35.	A. V. Pukhlikov, “Birational geometry of Fano double covers”, Sb. Math., 199:8 (2008), 1225–1250
36.	A. V. Pukhlikov, “Explicit examples of birationally rigid Fano varieties”, Mosc. Math. J., 7:3 (2007), 543–560	1 ^[x]
37.	A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
38.	A. V. Pukhlikov, “Kvadratichnye metody v teorii optimalnogo upravleniya i teorii sistem”, Nelineinaya dinamika i upravlenie, 5, Fizmatlit, M., 2007, 69–98
39.	A. V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526	23 ^[x]
40.	A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368
41.	A. V. Pukhlikov, “Geometry of discontinuous systems near a manifold of singularities of third order”, Differ. Equ., 41:12 (2005), 1710–1716
42.	A. V. Pukhlikov, “Biratsionalno zhestkie pryamye proizvedeniya Fano”, Dokl. RAN, 401:2 (2005), 163–165
43.	A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255
44.	A. V. Pukhlikov, “Birationally rigid Fano varieties”, The Fano Conference, Univ. Torino, Turin, 2004, 659–681
45.	A. V. Pukhlikov, “Optimal control of distributions”, Nonlinear dynamics and control. 2, Comput. Math. Model., 15:3 (2004), 223–256
46.	A. V. Pukhlikov, “Integral representations in the theory of controlled systems”, Nonlinear dynamics and control, Comput. Math. Model., 18, no. 4, 2007, 344–368
47.	A. V. Pukhlikov, “Fano direct products as rationally connected fibrations”, J. Math. Sci., 140:2 (2007), 303–320
48.	A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702
49.	A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071
50.	A. V. Pukhlikov, “Birationally rigid singular Fano hypersurfaces”, Algebraic geometry, 12, J. Math. Sci. (N. Y.), 115:3 (2003), 2428–2436	8 ^[x]
51.	A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596
52.	A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano hypersurfaces”, Dokl. Akad. Nauk, 385:1 (2002), 28–30
53.	A. V. Pukhlikov, “Discontinuous dynamical systems in optimal control theory”, Nonlinear dynamics and control, Comput. Math. Model., 13:1 (2002), 81–105
54.	A. V. Pukhlikov, “Birational Automorphisms of Algebraic Varieties with a Pencil of Fano Double Covers”, Funct. Anal. Appl., 36:1 (2002), 74–75
55.	A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces”, Izv. Math., 66:6 (2002), 1243–1269
56.	A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces with singularities”, Russian Math. Surveys, 57:1 (2002), 157–158
57.	F. Campana, Th. Peternell, A. V. Pukhlikov, “Generalized Tsen's theorem and rationally connected Fano fibrations”, Sb. Math., 193:10 (2002), 1443–1468
58.	A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces with isolated singularities”, Sb. Math., 193:3 (2002), 445–471
59.	F. Kampana, T. Peternell, A. V. Pukhlikov, “Obobschennaya teorema Tzena i ratsionalno svyaznye mnogoobraziya”, Dokl. RAN, 381:6 (2001), 742–744
60.	A. V. Pukhlikov, “Birationally rigid Fano complete intersections”, J. Reine Angew. Math., 541 (2001), 55–79	34 ^[x]
61.	A. V. Pukhlikov, “Singularities in discontinuous dynamical systems”, Dokl. Akad. Nauk, 378:4 (2001), 456–458
62.	A. V. Pukhlikov, “The geometry of discontinuous systems near a hyperbolic singular point of a sliding field”, Differ. Equ., 37:3 (2001), 377–400
63.	A. V. Pukhlikov, “Birational automorphisms of double spaces with singularities”, J. Math. Sci. (New York), 85:4 (1997), 2128–2141
64.	V. A. Iskovskikh, A. V. Pukhlikov, “Birational automorphisms of multidimensional algebraic manifolds”, J. Math. Sci., 82:4 (1996), 3528–3613
65.	A. Corti, A. Pukhlikov, M. Reid, “Fano 3-fold hypersurfaces”, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000, 175–258
66.	A. V. Pukhlikov, “Essentials of the method of maximal singularities”, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, Cambridge Univ. Press, Cambridge, 2000, 73–100
67.	A. V. Pukhlikov, “Biratsionalnye avtomorfizmy polnykh peresechenii Fano”, Doklady Akademii nauk, 374:2 (2000), 160–163
68.	A. V. Pukhlikov, “A Gauss–Ostrogradskii theorem for integral transforms over the Euler characteristic”, Integral Transform. Spec. Funct., 9:4 (2000), 299–312	1 ^[x]
69.	A. V. Pukhlikov, “Birationally rigid Fano fibrations”, Izv. Math., 64:3 (2000), 563–581
70.	A. V. Pukhlikov, “Fiber-wise birational correspondences”, Math. Notes, 68:1 (2000), 103–112
71.	A. V. Pukhlikov, “Birational automorphisms of algebraic varieties with a pencil of double quadrics”, Math. Notes, 67:2 (2000), 192–199
72.	A. V. Pukhlikov, “Birationally rigid Fano double hypersurfaces”, Sb. Math., 191:6 (2000), 883–908
73.	A. V. Pukhlikov, “Geometry of discontinuous systems near an elliptic singularity”, Differential Equations, 35:11 (1999), 1516–1529 (2000)
74.	A. V. Pukhlikov, “Structurally stable singularities of discontinuous dynamical systems”, Differential Equations, 35:5 (1999), 675–682
75.	A. V. Pukhlikov, “Certain examples of birationally rigid varieties with a pencil of double quadrics”, Algebraic geometry, 9, J. Math. Sci. (New York), 94:1 (1999), 986–995	11 ^[x]
76.	A. V. Pukhlikov, “Birational Automorphisms of Fano Double Covers”, Funct. Anal. Appl., 33:4 (1999), 313–314
77.	A. V. Pukhlikov, “Birationally rigid varieties with a sheaf of Fano hypersurfaces”, Russian Math. Surveys, 54:1 (1999), 260–261
78.	A. V. Pukhlikov, “Optimal bilinear systems on a plane”, Differential Equations, 34:11 (1998), 1516–1521 (1999)
79.	A. V. Pukhlikov, “Birational automorphisms of three-dimensional algebraic varieties fibered by Del Pezzo surfaces”, Dokl. Akad. Nauk, 361:1 (1998), 14–16
80.	A. V. Pukhlikov, “The discrete maximum principle”, Dokl. Akad. Nauk, 360:6 (1998), 747–749	1 ^[x]
81.	A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces”, Invent. Math., 134:2 (1998), 401–426	101 ^[x]
82.	A. V. Pukhlikov, “Birational automorphisms of higher-dimensional algebraic varieties”, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math., Extra Vol. II, 1998, 97–107 (electronic)
83.	A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155
84.	A. V. Pukhlikov, “Integral transformations in the theory of controllable dynamic systems”, Dokl. Math., 55:2 (1997), 315–317
85.	A. V. Pukhlikov, “Integral representations in the theory of discrete controllable systems”, Dokl. Math., 55:2 (1997), 312–314
86.	A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds fibred by cubic surfaces”, Russian Math. Surveys, 52:1 (1997), 230–231
87.	A. V. Pukhlikov, “Fredholm determinants and the Newton method in problems of the control of distributions”, Automat. Remote Control, 57:6 (1996), 814–818
88.	A. V. Pukhlikov, “Singular regimes in problems of the control of distributions. I. Scalar controls”, Automat. Remote Control, 57:5 (1996), 634–643
89.	A. V. Pukhlikov, “Degenerations of Hamiltonian structures in optimal control problems”, Differential Equations, 31:11 (1995), 1841–1847 (1996)
90.	A. V. Pukhlikov, “Analytic representations in problems of the control of distributions”, Automat. Remote Control, 56:12 (1995), 1698–1708 (1996)
91.	A. V. Pukhlikov, “Rational curves with prescribed branches”, Moscow Univ. Math. Bull., 50:1 (1995), 20–22
92.	A. V. Pukhlikov, “Hamiltonian structures in optimal control theory”, J. Dynam. Control Systems, 1:3 (1995), 379–401	5 ^[x]
93.	A. V. Pukhlikov, “Problems of the control of distributions in dynamical systems”, Automat. Remote Control, 56:4 (1995), 517–525
94.	A. V. Pukhlikov, “A remark on the theorem of V. A. Iskovskikh and Yu. I. Manin on a three-dimensional quartic”, Proc. Steklov Inst. Math., 208 (1995), 244–254
95.	A. V. Pukhlikov, “Liouville's theorem in optimal control problems”, Differential Equations, 30:11 (1994), 1808–1814 (1995)
96.	A. G. Khovanskii, A. V. Pukhlikov, “Integral transforms based on Euler characteristic and their applications”, Integral Transform. Spec. Funct., 1:1 (1993), 19–26	5 ^[x]
97.	A. V. Pukhlikov, “Poisson's theorem in optimal control problems”, Differential Equations, 29:11 (1993), 1685–1690 (1994)
98.	A. I. Propoĭ, A. V. Pukhlikov, “Quadratic approximation in nonlinear extremal problems”, Phys. Dokl., 38:8 (1993), 320–322 (1994)
99.	V. A. Iskovskih, A. V. Pukhlikov, “Birational automorphisms of Fano varieties”, Geometry of complex projective varieties (Cetraro, 1990), Sem. Conf., 9, Mediterranean, Rende, 1993, 191–201
100.	A. V. Pukhlikov, “Asymptotically periodic systems. II”, Autom. Remote Control, 54:10 (1993), 1493–1503
101.	A. V. Pukhlikov, “Asymptotically periodic systems. I”, Autom. Remote Control, 54:5 (1993), 747–754
102.	A. I. Propoǐ, A. V. Pukhlikov, “The stochastic Newton method in nonlinear extremal problems”, Autom. Remote Control, 54:4 (1993), 605–613
103.	A. V. Pukhlikov, A. G. Khovanskii, “Finitely additive measures of virtual polyhedra”, St. Petersburg Math. J., 4:2 (1993), 337–356
104.	A. V. Pukhlikov, A. G. Khovanskii, “The Riemann–Roch theorem for integrals and sums of quasipolynomials on virtual polytopes”, St. Petersburg Math. J., 4:4 (1993), 789–812
105.	A. V. Pukhlikov, “Maximal singularities on the Fano variety $V_6^3$”, Moscow Univ. Math. Bull., 44:2 (1989), 70–75
106.	A. V. Pukhlikov, “Birational automorphisms of a double space and double quadric”, Math. USSR-Izv., 32:1 (1989), 233–243
107.	A. V. Pukhlikov, “Birational automorphisms of a three-dimensional quartic with a quadratic singularity”, Math. USSR-Sb., 63:2 (1989), 457–482
108.	A. V. Pukhlikov, “Birational isomorphisms of four-dimensional quintics”, Invent. Math., 87:2 (1987), 303–329	43 ^[x]
109.	A. V. Pukhlikov, “Birational automorphisms of four-dimensional quintics”, Moscow University Math. Bulletin, 1986, no. 2, 10–15
Books

110.	A. Pukhlikov, Birationally Rigid Varieties, Mathematical Surveys and Monographs, 190, Amer. Math. Soc., Providence, RI, 2013 , 367 pp.	42 ^[x]
Popular science or education materials

111.	A. V. Pukhlikov, Mat. Pros., 1, MCCME, Moscow, 1997, 85–89
Personalia

112.	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
113.	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

Presentations in Math-Net.Ru

1.	Rationally connected rational double covers of primitive Fano varieties A. V. Pukhlikov One-day conference dedicated to the memory of V. A. Iskovskikh December 22, 2020 13:30
2.	Бирациональная геометрия особых гиперповерхностей Фано индекса два A. V. Pukhlikov Shafarevich Seminar December 4, 2018 15:00
3.	The $4n^2$-inequality for complete intersection singularities A. V. Pukhlikov Shafarevich Seminar December 13, 2016 15:00
4.	Бирациональная геометрия многообразий, расслоенных на двойные пространства Фано A. V. Pukhlikov Shafarevich Seminar March 29, 2016 15:00
5.	Бирационально жесткие расслоения Фано A. V. Pukhlikov Shafarevich Seminar April 14, 2015 15:00
6.	Бирационально жесткие расслоения Фано Alexander Pukhlikov Annual memorial conference dedicated to the memory of Andrei Nikolaevich Tyurin October 28, 2014 11:40
7.	Бирациональная геометрия гиперповерхностей Фано индекса два A. V. Pukhlikov Shafarevich Seminar April 15, 2014 15:00
8.	Birational geometry of Fano hypersurfaces of index two A. V. Pukhlikov International conference "Geometry of Algebraic Varieties" dedicated to the memory of V. A. Iskovskikh October 22, 2013 15:00
9.	Бирационально жесткие многомерные многообразия Фано A. V. Pukhlikov International conference dedicated to the 90th anniversary of academician Igor Rostislavovich Shafarevich June 5, 2013 10:30
10.	Birationally rigid Fano complete intersections A. V. Pukhlikov Shafarevich Seminar March 27, 2012 15:00
11.	K-тривиальные структуры на полных пересечениях Фано A. V. Pukhlikov Seminar by Algebra Department April 12, 2011 15:00
12.	Birational geometry of Fano double spaces of index two A. V. Pukhlikov International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh June 29, 2009 16:30
13.	Бирациональная геометрия двойных пространств индекса два A. V. Pukhlikov Seminar by Algebra Department June 16, 2009 15:00
14.	Бирационально жесткие многообразия A. V. Pukhlikov Seminar by Algebra Department November 18, 2008 15:00

Books in Math-Net.Ru

A. V. Pukhlikov, Birational Geometry of Higher-Dimensional Fano Varieties, Sovrem. Probl. Mat., 19, 2014, 174 с.
http://mi.mathnet.ru/book1513

Organisations

Articles

Books

Popular science or education materials

Personalia