Торические и сферические многообразия, рациональные точки на алгебраичеких многообразиях, многообразия Фано, многообразия Калаби-Яу, зеркальная симметрия, выпуклые многогранники.
Научная биография:
Закончил механико-математический факультет МГУ им. Ломоносова в 1983 году. С 1983 по 1991 год работал на кафедре высшей алгебры механико-математического факультета МГУ. Кандидатская диссертация по теме "Многомерные торические многообразия с положительным антиканоническим классом" (1985), научный руководитель В.А. Исковских. С 1991 по 1996 год научный сотрудник математического факультета университета города Эссен. Докторская диссертации (Habilitation,1993) по теме "Hodge Theory of Hypersurfaces in Toric Varieties and Recent Developments in Quantum Physics" награждена премией
(Heinz Maier-Leibnitz-Preis 1995). С 1994 по 1996 год стипендия имени Гейзерберга Немецкого Исследовательского Общества. С 1996 года профессор кафедры алгебры математического факультета университета города Тюбинген.
Приглашенный докладчик по теме " Mirror Symmetry and Toric Geometry" на Международном математическом конгрессе в Берлине (1998). Член Гейдельбергской академии наук с 2003 года.
Основные публикации:
Batyrev, V. V. and Manin, Yu. I., “Sur le nombre des points rationnels de hauteur borné des variétés algébriques”, Math. Ann., 286:1-3 (1990), 27–43
Batyrev, Victor V., “Variations of the mixed Hodge structure of affine
hypersurfaces in algebraic tori”, Duke Math. J., 69:2 (1993), 349–409
Batyrev, Victor V., “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, J. Algebraic Geom., 3:3 (1994), 493–535
Batyrev, Victor V. and Tschinkel, Yuri, “Manin's conjecture for toric varieties”, J. Algebraic Geom., 7:1 (1998), 15–53
Batyrev, Victor V., “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, J. Eur. Math. Soc., 1:1 (1999), 5–33
V. Batyrev, I. Ciocan-Fontanine, B. Kim, D. van Straten, “Mirror symmetry and toric degenerations of partial flag manifolds”, Acta Mathematica, 184:1 (2000), 1–39
V. Batyrev, D. van Straten, “Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties”, Comm. Math. Phys., 168:3 (1995), 493–533
V. Batyrev, I. Ciocan-Fontanine, B. Kim, D. van Straten, “Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians”, Nuclear Phys. B, 514:3 (1998), 640–666
Victor Batyrev, “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, Journal of the European Mathematical Society, 1:1 (1999), 5–33
В. В. Батырев, “Трехмерные торические многообразия Фано”, Изв. АН СССР. Сер. матем., 45:4 (1981), 704–717; V. V. Batyrev, “Toroidal Fano 3-folds”, Math. USSR-Izv., 19:1 (1982), 13–25
V. Batyrev, O. Popov, “The Cox ring of a del Pezzo surface”, Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), Progr. Math., 226, Birkhäuser Boston, Boston, MA, 2004, 85–103
В. В. Батырев, Ю. Чинкель, “Высотные дзета-функции торических многообразий”, Алгебраическая геометрия – 5, Итоги науки и техн. Сер. Соврем. мат. и ее прил. Темат. обз., 34, ВИНИТИ, М., 2001, 164–194; V. V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, J. Math. Sci., 82:1 (1996), 3220–3239
V. Batyrev, M. Kreuzer, “Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions”, Advances in Theoretical and Mathematical Physics, 14:3 (2010), 879–898
V. Batyrev, M. Blume, “The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces”, The Tohoku Mathematical Journal. Second Series, 63:4 (2011), 581–604
В. В. Батырев, К. Шаллер, “Струнные $E$-функции канонических торических трехмерных многообразий Фано и их приложения”, Изв. РАН. Сер. матем., 83:4 (2019), 26–49; V. V. Batyrev, K. Schaller, “Stringy $E$-functions of canonical toric Fano threefolds and their applications”, Izv. Math., 83:4 (2019), 676–697
В. В. Батырев, “О некоторых численных характеристиках многомерных многообразий Фано”, Изв. АН СССР. Сер. матем., 49:2 (1985), 445–459; V. V. Batyrev, “On some numerical characteristics of multidimensional Fano varieties”, Math. USSR-Izv., 26:2 (1986), 423–435
Victor Batyrev, The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality, 2017 (Published online) , 35 pp., arXiv: 1707.02602
30.
V. Batyrev, G. Gagliardi, “On the algebraic stringy Euler number”, Proc. Amer. Math. Soc., 145 (2017), 1–13 (to appear)
31.
V. Batyrev, A. Moreau, Satellites of spherical subgroups, 2016 (Published online) , 39 pp., arXiv: 1610.07377
32.
V. Batyrev, M. Kreuzer, “Conifold degenerations of Fano 3-folds as hypersurfaces in toric varieties”, Strings, gauge fields, and the geometry behind, World Sci. Publ., Hackensack, NJ, 2013, 187–212
33.
V. Batyrev, J. Hofscheier, Lattice polytopes, finite abelian subgroups in $\operatorname{SL}(n)$ and coding theory, 2013 (Published online) , 18 pp., arXiv: 1309.5312
34.
K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held April 15–21, 2012.”, Oberwolfach Reports, 9:2 (2012), 1231–1306
35.
V. Batyrev, J. Hofscheier, A generalization of a theorem of G. K. White, 2010 (Published online) , 12 pp., arXiv: 1004.3411
36.
K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held January 4th – January 10th, 2009.”, Oberwolfach Reports, 6:1 (2009), 5–74
37.
Victor Batyrev, “Lattice polytopes with a given $h^*$-polynomial”, Algebraic and geometric combinatorics, 423, Amer. Math. Soc., Providence, RI, 2006, 1–10 (to appear)
38.
K. Altmann, V. Batyrev, B. Tessier, “Report 5/2006: Convex and Algebraic Geometry (January 29th – February 4th, 2006)”, Oberwolfach Reports, 3:1 (2006), 253–316
39.
Victor Batyrev, “Toric degenerations of Fano varieties and constructing mirror manifolds”, The Fano Conference, Univ. Torino, Turin, 2004, 109–122
40.
V. Batyrev, E. Materov, “Mixed toric residues and Calabi-Yau complete intersections”, Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001), Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI, 2003, 3–26
41.
Victor Batyrev, “Stringy Hodge numbers and Virasoro algebra”, Mathematical Research Letters, 7:2-3 (2000), 155–164
42.
Victor Batyrev, Canonical abelianization of finite group actions, 2000 (Published online) , 4 pp., arXiv: math/0009043
43.
Victor Batyrev, “Birational Calabi-Yau $n$-folds have equal Betti numbers”, New trends in algebraic geometry (Warwick, 1996), London Math. Soc. Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999, 1–11
44.
Victor Batyrev, “Mirror symmetry and toric geometry”, Documenta Mathematica, 1998, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 239–248
45.
V. Batyrev, Ju. Tschinkel, “Manin's conjecture for toric varieties”, Journal of Algebraic Geometry, 7:1 (1998), 15–53
46.
Victor Batyrev, “Stringy Hodge numbers of varieties with Gorenstein canonical singularities”, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publ., River Edge, NJ, 1998, 1–32
47.
V. Batyrev, Yu. Tschinkel, “Tamagawa numbers of polarized algebraic varieties”, Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, 251, Soc. Math. France, 1998, 299–340
48.
V. Batyrev, L. Borisov, “Dual cones and mirror symmetry for generalized Calabi-Yau manifolds”, Mirror symmetry, II, Amer. Math. Soc., Providence, RI, 1997, 71–86
49.
V. Batyrev, Yu. Tschinkel, “Rational points on some Fano cubic bundles”, C. R. Acad. Sci. Paris Sér. I Math., 323:1 (1996), 41–46
50.
V. Batyrev, L. Borisov, “On Calabi-Yau complete intersections in toric varieties”, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 39–65
51.
V. Batyrev, Yu. Tschinkel, “Rational points on toric varieties”, Number theory (Halifax, NS, 1994), CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI, 1995, 39–48
52.
Victor Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, Journal of Algebraic Geometry, 3:3 (1994), 493–535
53.
Victor Batyrev, “Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori”, Duke Math. J., 169 (1993), 349–409
54.
Victor Batyrev, “Quantum cohomology rings of toric manifolds”, Journées de Géométrie Algébrique d'Orsay (Orsay, 1992), Astérisque, 218, Soc. Math. France, 1993, 9–34
55.
Victor Batyrev, “The cone of effective divisors of threefolds”, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989), Contemp. Math., 131, Amer. Math. Soc., Providence, RI, 1992, 337–352
56.
Victor Batyrev, “On the classification of smooth projective toric varieties”, The Tohoku Mathematical Journal. Second Series, 43:4 (1991), 569–585
57.
Батырев В.В., Мельников Д.А., “Теорема о непродолжимости торических многообразий”, Вестник Московского Университета, серия мат. и мех., 1986, № 3, 20–24