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

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


2025
1.	A. V. Pukhlikov, “Affine Complements in the Projective Space with Trivial Automorphism Group”, Proc. Steklov Inst. Math., 329 (2025), 207–216

2024
2.	A. V. Pukhlikov, “Birationally rigid hypersurfaces with quadratic singularities of low rank”, Sb. Math., 215:6 (2024), 823–840

2022
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

2021
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

2019
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

2018
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]

2017
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

2016
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

2015
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

2014
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]

2015
21.	A. V. Pukhlikov, “Birational Geometry of Higher-Dimensional Fano Varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150

2014
22.	A. V. Pukhlikov, “Birationally rigid Fano complete intersections. II”, J. Reine Angew. Math., 2014:688 (2014), 209–218	7 ^[x]

2013
23.	A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845
24.	A. Pukhlikov, Birationally Rigid Varieties, Mathematical Surveys and Monographs, 190, Amer. Math. Soc., Providence, RI, 2013 , 367 pp.	42 ^[x]
25.	A. V. Pukhlikov, “Birational rigidity of Fano complete intersections”, Dokl. Math., 87:1 (2013), 34–35

2012
26.	A. V. Pukhlikov, “$K$-Trivial Structures on Fano Complete Intersections”, Math. Notes, 91:4 (2012), 568–574
27.	A. V. Pukhlikov, “On the multiplicity of solutions of a system of algebraic equations”, Proc. Steklov Inst. Math., 276 (2012), 234–249

2010
28.	A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991
29.	A. V. Pukhlikov, “Existence of the Kähler–Einstein Metric on Certain Fano Complete Intersections”, Math. Notes, 88:4 (2010), 552–558
30.	A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171

2009
31.	A. V. Pukhlikov, “Rationality problem and birational rigidity”, Cohomological and geometric approaches to rationality problems, Progr. Math., 282, Birkhäuser, Boston, 2009, 275–311
32.	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]
33.	A. V. Pukhlikov, “Singularities of Algebraic Subvarieties and Problems of Birational Geometry”, Proc. Steklov Inst. Math., 267 (2009), 235–247
34.	A. V. Pukhlikov, “Birational Geometry of Singular Fano Varieties”, Proc. Steklov Inst. Math., 264 (2009), 159–177

2010
35.	A. V. Pukhlikov, “On the self-intersection of a movable linear system”, J. Math. Sci., 164:1 (2010), 119–130

2008
36.	A. V. Pukhlikov, “Birational geometry of Fano double covers”, Sb. Math., 199:8 (2008), 1225–1250

2007
37.	A. V. Pukhlikov, “Explicit examples of birationally rigid Fano varieties”, Mosc. Math. J., 7:3 (2007), 543–560	1 ^[x]
38.	A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
39.	A. V. Pukhlikov, “Kvadratichnye metody v teorii optimalnogo upravleniya i teorii sistem”, Nelineinaya dinamika i upravlenie, 5, Fizmatlit, M., 2007, 69–98

2006
40.	A. V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526	23 ^[x]
41.	A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368

2005
42.	A. V. Pukhlikov, “Geometry of discontinuous systems near a manifold of singularities of third order”, Differ. Equ., 41:12 (2005), 1710–1716
43.	A. V. Pukhlikov, “Biratsionalno zhestkie pryamye proizvedeniya Fano”, Dokl. RAN, 401:2 (2005), 163–165
44.	A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255

2004
45.	A. V. Pukhlikov, “Birationally rigid Fano varieties”, The Fano Conference, Univ. Torino, Turin, 2004, 659–681
46.	A. V. Pukhlikov, “Optimal control of distributions”, Nonlinear dynamics and control. 2, Comput. Math. Model., 15:3 (2004), 223–256

2007
47.	A. V. Pukhlikov, “Integral representations in the theory of controlled systems”, Nonlinear dynamics and control, Comput. Math. Model., 18, no. 4, 2007, 344–368
48.	A. V. Pukhlikov, “Fano direct products as rationally connected fibrations”, J. Math. Sci., 140:2 (2007), 303–320

2004
49.	A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702
50.	A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071

2003
51.	A. V. Pukhlikov, “Birationally rigid singular Fano hypersurfaces”, Algebraic geometry, 12, J. Math. Sci. (N. Y.), 115:3 (2003), 2428–2436	8 ^[x]
52.	A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596

2002
53.	A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano hypersurfaces”, Dokl. Akad. Nauk, 385:1 (2002), 28–30
54.	A. V. Pukhlikov, “Discontinuous dynamical systems in optimal control theory”, Nonlinear dynamics and control, Comput. Math. Model., 13:1 (2002), 81–105
55.	A. V. Pukhlikov, “Birational Automorphisms of Algebraic Varieties with a Pencil of Fano Double Covers”, Funct. Anal. Appl., 36:1 (2002), 74–75
56.	A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces”, Izv. Math., 66:6 (2002), 1243–1269
57.	A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces with singularities”, Russian Math. Surveys, 57:1 (2002), 157–158
58.	F. Campana, Th. Peternell, A. V. Pukhlikov, “Generalized Tsen's theorem and rationally connected Fano fibrations”, Sb. Math., 193:10 (2002), 1443–1468
59.	A. V. Pukhlikov, “Birationally rigid Fano hypersurfaces with isolated singularities”, Sb. Math., 193:3 (2002), 445–471

2001
60.	F. Kampana, T. Peternell, A. V. Pukhlikov, “Obobschennaya teorema Tzena i ratsionalno svyaznye mnogoobraziya”, Dokl. RAN, 381:6 (2001), 742–744
61.	A. V. Pukhlikov, “Birationally rigid Fano complete intersections”, J. Reine Angew. Math., 541 (2001), 55–79	34 ^[x]
62.	A. V. Pukhlikov, “Singularities in discontinuous dynamical systems”, Dokl. Akad. Nauk, 378:4 (2001), 456–458
63.	A. V. Pukhlikov, “The geometry of discontinuous systems near a hyperbolic singular point of a sliding field”, Differ. Equ., 37:3 (2001), 377–400

1997
64.	A. V. Pukhlikov, “Birational automorphisms of double spaces with singularities”, J. Math. Sci. (New York), 85:4 (1997), 2128–2141

1996
65.	V. A. Iskovskikh, A. V. Pukhlikov, “Birational automorphisms of multidimensional algebraic manifolds”, J. Math. Sci., 82:4 (1996), 3528–3613

2000
66.	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
67.	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
68.	A. V. Pukhlikov, “Biratsionalnye avtomorfizmy polnykh peresechenii Fano”, Doklady Akademii nauk, 374:2 (2000), 160–163
69.	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]
70.	A. V. Pukhlikov, “Birationally rigid Fano fibrations”, Izv. Math., 64:3 (2000), 563–581
71.	A. V. Pukhlikov, “Fiber-wise birational correspondences”, Math. Notes, 68:1 (2000), 103–112
72.	A. V. Pukhlikov, “Birational automorphisms of algebraic varieties with a pencil of double quadrics”, Math. Notes, 67:2 (2000), 192–199
73.	A. V. Pukhlikov, “Birationally rigid Fano double hypersurfaces”, Sb. Math., 191:6 (2000), 883–908

1999
74.	A. V. Pukhlikov, “Geometry of discontinuous systems near an elliptic singularity”, Differential Equations, 35:11 (1999), 1516–1529 (2000)
75.	A. V. Pukhlikov, “Structurally stable singularities of discontinuous dynamical systems”, Differential Equations, 35:5 (1999), 675–682
76.	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]
77.	A. V. Pukhlikov, “Birational Automorphisms of Fano Double Covers”, Funct. Anal. Appl., 33:4 (1999), 313–314
78.	A. V. Pukhlikov, “Birationally rigid varieties with a sheaf of Fano hypersurfaces”, Russian Math. Surveys, 54:1 (1999), 260–261

1998
79.	A. V. Pukhlikov, “Optimal bilinear systems on a plane”, Differential Equations, 34:11 (1998), 1516–1521 (1999)
80.	A. V. Pukhlikov, “Birational automorphisms of three-dimensional algebraic varieties fibered by Del Pezzo surfaces”, Dokl. Akad. Nauk, 361:1 (1998), 14–16
81.	A. V. Pukhlikov, “The discrete maximum principle”, Dokl. Akad. Nauk, 360:6 (1998), 747–749	1 ^[x]
82.	A. V. Pukhlikov, “Birational automorphisms of Fano hypersurfaces”, Invent. Math., 134:2 (1998), 401–426	101 ^[x]
83.	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)
84.	A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155

1997
85.	A. V. Pukhlikov, “Integral transformations in the theory of controllable dynamic systems”, Dokl. Math., 55:2 (1997), 315–317
86.	A. V. Pukhlikov, “Integral representations in the theory of discrete controllable systems”, Dokl. Math., 55:2 (1997), 312–314
87.	A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds fibred by cubic surfaces”, Russian Math. Surveys, 52:1 (1997), 230–231

1996
88.	A. V. Pukhlikov, “Fredholm determinants and the Newton method in problems of the control of distributions”, Automat. Remote Control, 57:6 (1996), 814–818
89.	A. V. Pukhlikov, “Singular regimes in problems of the control of distributions. I. Scalar controls”, Automat. Remote Control, 57:5 (1996), 634–643

1995
90.	A. V. Pukhlikov, “Degenerations of Hamiltonian structures in optimal control problems”, Differential Equations, 31:11 (1995), 1841–1847 (1996)
91.	A. V. Pukhlikov, “Analytic representations in problems of the control of distributions”, Automat. Remote Control, 56:12 (1995), 1698–1708 (1996)
92.	A. V. Pukhlikov, “Rational curves with prescribed branches”, Moscow Univ. Math. Bull., 50:1 (1995), 20–22
93.	A. V. Pukhlikov, “Hamiltonian structures in optimal control theory”, J. Dynam. Control Systems, 1:3 (1995), 379–401	5 ^[x]
94.	A. V. Pukhlikov, “Problems of the control of distributions in dynamical systems”, Automat. Remote Control, 56:4 (1995), 517–525
95.	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

1994
96.	A. V. Pukhlikov, “Liouville's theorem in optimal control problems”, Differential Equations, 30:11 (1994), 1808–1814 (1995)

1993
97.	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]
98.	A. V. Pukhlikov, “Poisson's theorem in optimal control problems”, Differential Equations, 29:11 (1993), 1685–1690 (1994)
99.	A. I. Propoĭ, A. V. Pukhlikov, “Quadratic approximation in nonlinear extremal problems”, Phys. Dokl., 38:8 (1993), 320–322 (1994)
100.	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
101.	A. V. Pukhlikov, “Asymptotically periodic systems. II”, Autom. Remote Control, 54:10 (1993), 1493–1503
102.	A. V. Pukhlikov, “Asymptotically periodic systems. I”, Autom. Remote Control, 54:5 (1993), 747–754
103.	A. I. Propoǐ, A. V. Pukhlikov, “The stochastic Newton method in nonlinear extremal problems”, Autom. Remote Control, 54:4 (1993), 605–613
104.	A. V. Pukhlikov, A. G. Khovanskii, “Finitely additive measures of virtual polyhedra”, St. Petersburg Math. J., 4:2 (1993), 337–356
105.	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

1989
106.	A. V. Pukhlikov, “Maximal singularities on the Fano variety $V_6^3$”, Moscow Univ. Math. Bull., 44:2 (1989), 70–75
107.	A. V. Pukhlikov, “Birational automorphisms of a double space and double quadric”, Math. USSR-Izv., 32:1 (1989), 233–243
108.	A. V. Pukhlikov, “Birational automorphisms of a three-dimensional quartic with a quadratic singularity”, Math. USSR-Sb., 63:2 (1989), 457–482

1987
109.	A. V. Pukhlikov, “Birational isomorphisms of four-dimensional quintics”, Invent. Math., 87:2 (1987), 303–329	43 ^[x]

1986
110.	A. V. Pukhlikov, “Birational automorphisms of four-dimensional quintics”, Moscow University Math. Bulletin, 1986, no. 2, 10–15

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