Богомолов Федор Алексеевич
Лаборатория алгебраической геометрии и ее приложений
Профессиональные интересы
Должности
- научный руководитель — Лаборатория алгебраической геометрии и ее приложений
Био
- · Начал работать в НИУ ВШЭ в 2010 году.
- · Научно-педагогический стаж: 15 лет.
Образование
- 1983 · Доктор физико-математических наук
- 1970 · Специалитет: Московский государственный университет им. М.В. Ломоносова, специальность «Математика», квалификация «Математик»
Опыт работы
- · 2010 г.: с Научный руководитель, Лаборатория алгебраической геометрии и ее приложений
Награды и поощрения
- · Silver Professor New York University (2016)
- · Почетная грамота Высшей школы экономики (октябрь 2021)
- · Благодарственное письмо ректора НИУ ВШЭ (сентябрь 2021)
- · Медаль "За вклад в науку и просвещение" (октябрь 2017)
- · Благодарность Высшей школы экономики (ноябрь 2016)
Гранты и проекты
- — · Совет по грантам Правительства РФ продлил еще на два года финансирование двух международных лабораторий ВШЭ, возглавляемых ведущими зарубежными учеными — Лаборатории сравнительных социальных исследований и Лаборатории алгебраической геометрии и ее приложений.
Конференции (36)
Показать все
- · 2021: Семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: О некоторых вопросах комплексной и арифметической геометрии II
- · 2021: Summer Geometry Fest (Moscow). Доклад: Second Chern classes of vector bundles and related geometry
- · 2020: Семинар Лаборатории алгебраической геометрии (Москва). Доклад: Several remarks on results in group theory and represnetation theory of finite groups
- · 2019: Семинар лаборатории алгебраической геометрии (Москва). Доклад: On base varieties of lagrangian abelian fibrations on projective hyperkahler manifolds
- · 2019: "Birational Geometry and Fano varieties" dedicated to V. Iskovskikh (Москва). Доклад: Group theoretic prove of the classification ofVII0surfaces with b2= 0
- · 2019: Летняя математическая школа Алгебра и Теория Чисел (Вороново). Доклад: Некоторые вопросы теории эллиптических кривых
- · 2019: Семинар лаборатории алгебраической геометрии (Москва). Доклад: On some problems in algebraic geometry and related areas
- · 2019: Современная геометрия и ее приложения - 2019 (Казань). Доклад: Некоторые открытые проблемы в комплексной и алгебраической геометрии
- · 2018: Семинар лаборатории алгебраической геометрии (Москва). Доклад: Абелевы расслоения
- · 2018: Семинар лаборатории алгебраической геометрии (Москва). Доклад: On $j$ invariants of the projective images of $4$-tuples torsion points
- · 2018: Geometry at Large, Symmetries and Correspondences ("Геометрия в целом, симметрии и соответствия") (Фуэртевентура). Доклад: On geometry over small fields ("O геометрии над малыми полями")
- · 2018: Geometry at Large, Symmetries and Correspondences ("Геометрия в целом, симметрии и соответствия") (Фуэртевентура). Доклад: Projective invariants of collections of torsion points of elliptic curves (Проективные инварианты наборов точек кручения на эллиптических кривых)
- · 2017: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: Geometry of sets of torsion points on elliptic curves
- · 2017: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: Комплексные поверхности типа VII_0 и теория групп
- · 2017: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: $PGL(2)$-invariants of collections of torsion points of elliptic curves
- · 2016: 2-я МЕЖДУНАРОДНАЯ НАУЧНАЯ КОНФЕРЕНЦИЯ - НАУКА БУДУЩЕГО (Казань). Доклад: Algebraic geometry
- · 2016: Workshop on Algebraic Geometry (Ханга Роа). Доклад: LEMMA ON INTERSECTION OF CURVES AND DOMAINS IN COMPLEX PROJECTIVE VARIETIES AND APPLICATIONS
- · 2016: Еженедельный семинар Лаборатории алгебраической геометрии (Москва). Доклад: I am going to consider the subsets of points in a complex projective line obtained as the image of torsion points under standard projection which is a quotient by the involution. These sets have finite intersections for different curves. Moreover I am going to show that in many cases the corresponding sets are quite small. I am also going to discuss some applications to geometry of hyperbolic curves.
- · 2016: Еженедельный семинар Лаборатории алгебраической геометрии (Москва). Доклад: Affine structures and VII_0 surfaces
- · 2015: Hyperbolicity in algebraic geometry (Ilhabela). Доклад: Closed symmetric differentials on projective surfaces
- · 2015: Magadan Algebraic Geometry International Conference (Магадан (Magadan)). Доклад: TORSION POINTS ON ELLIPTIC CURVES
- · 2015: Magadan Algebraic Geometry International Conference (Магадан (Magadan)). Доклад: SOME OPEN PROBLEMS IN ARITHMETIC ALGEBRAIC GEOMETRY
- · 2015: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Доклад: Torsion points on elliptic curves and related questions in algebra and geometry
- · 2014: Исследовательский семинар Университета Ноттингема (Nottingham). Доклад: Tate conjecture and relations in Galois groups
- · 2014: International conference "Algebraic Geometry and Number Theory" on the occasion of M.A. Tsfasman's and S.G. Vladuts' 60th birthday (Москва (Moscow)). Доклад: Homomorphisms of multiplicative groups of fields and section conjecture
- · 2014: Frontiers of Rationality (Longyearbyen). Доклад: Homomorphisms of Multyplicative Groups of Fields and Section Conjecture
- · 2014: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Closed symmetric differentials on surfaces
- · 2014: Symmetries and Correspondences: Higher Structures in Number Theory (Ноттингем (Nottingham)). Доклад: Projective geometry and non-archimedean valuations
- · 2014: Symmetries and correspondences in number theory, geometry, algebra, physics: intra-disciplinary trends (Ноттингем (Nottingham)). Доклад: On the section conjecture in anabelian geometry
- · 2014: Second ERC Research Period on Diophantine Geometry (Diophantine Geometry, Unlikely Intersections and Algebraic Dynamics) (Четраро (Cetraro)). Доклад: Braid group and Szpiroine quality
- · 2013: LMS Invited Lectures 2013: Fedor Bogomolov (Эдинбург). Доклад: Серия лекций "Birational Geometry and Galois Groups"
- · 2013: Международная конференция "Глобальные поля" (Москва). Доклад: Inducing nonramified cohomology elements
- · 2013: Workshop "Foliation Theory in Algebraic Geometry" (Нью-Йорк). Доклад: Closed symmetric differentials on surfaces
- · 2013: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: On Szpiro's conjecture, it's relation to ABC-conjecture and some other problems in arithmetic geometry
- · 2013: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Homomorphisms between multiplicative groups of fields and Grothendieck Section Conjecture
- · 2012: Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Доклад: Группы подстановок и проективные группы
Идентификаторы исследователя
- ORCID:
0000-0003-3464-6494 - ResearcherID:
J-2655-2015 - SPIN РИНЦ:
6211-4553 - Google Scholar: http://scholar.google.ru/citations?hl=ru&user=_kTMRyoAAAAJ&view_op=list_works&authuser=1
- Scopus AuthorID:
6603748855
Публикации (74)
Division polynomials and intersection of projective torsion points
2016 · ARTICLE · en
Given two elliptic curves, each of which is associated with a projection map that identifies opposite elements with respect to the natural group structure, we investigate how their corresponding projective images of torsion points intersect.
Families of disjoint divisors on varieties
2016 · ARTICLE · en
Following the work of Totaro and Pereira, we study sufficient conditions under which collections of pairwise-disjoint divisors on a variety over an algebraically closed field are contained in the fibers of a morphism to a curve. We prove that ρw(X)+1 pairwise-disjoint, connected divisors suffice for proper, normal varieties X, where ρw(X) is a modification of the Néron–Severi rank of X (they agree when X is projective and smooth). We then prove a strong counterexample in the affine case: if X is quasi-affine and of dimension ⩾ 2 over a countable, algebraically-closed field k, then there exists a (countable) collection of pairwise-disjoint divisors which cover the k-points of X, so that for any non-constant morphism from X to a curve, at most finitely many are contained in the fibers thereof. We show, however, that an uncountable collection of pairwise-disjoint, connected divisors in any normal variety over an algebraically-closed field must be contained in the fibers of a morphism to a curve.
On the Kobayashi pseudometric, complex automorphisms and hyperkaehler manifolds
2016 · PREPRINT · en
We define the Kobayashi quotient of a complex variety by identifying points with vanishing Kobayashi pseudodistance between them and show that if a compact complex manifold has an automorphism whose order is infinite, then the fibers of this quotient map are nontrivial. We prove that the Kobayashi quotients associated to ergodic complex structures on a compact manifold are isomorphic. We also give a proof of Kobayashi's conjecture on the vanishing of the pseudodistance for hyperk\"ahler manifolds having Lagrangian fibrations without multiple fibers in codimension one. For a hyperbolic automorphism of a hyperk\"ahler manifold, we prove that its cohomology eigenvalues are determined by its Hodge numbers, compute its dynamical degree and show that its cohomological trace grows exponentially, giving estimates on the number of its periodic points.
Abelian Calabi-Yau threefolds: Néron models and rational points
2016 · PREPRINT · en
We study Calabi-Yau threefolds fibered by abelian surfaces, in particular, their arithmetic properties, e.g., Neron models and Zariski density.
On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds
2016 в печати · CHAPTER · en
We define the Kobayashi quotient of a complex variety by identifying points with vanishing Kobayashi pseudodistance between them and show that if a complex projective manifold has an automorphism whose order is infinite, then the fibers of this quotient map are nontrivial. We prove that the Kobayashi quotients associated to ergodic complex structures on a compact manifold are isomorphic. We also give a proof of Kobayashi’s conjecture on the vanishing of the pseudodistance for hyperkähler manifolds having Lagrangian fibrations without multiple fibers in codimension one. For a hyperbolic automorphism of a hyperkähler manifold, we prove that its cohomology eigenvalues are determined by its Hodge numbers, compute its dynamical degree and show that its cohomological trace grows exponentially, giving estimates on the number of its periodic points.
The ambiguity index of an equipped finite group
2015 · ARTICLE · en
In \cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each equipped finite group $(G,O)$. It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group $G$ assuming that all local monodromies belong to conjugacy classes $O$ in $G$ and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (\cite{Kun1}, see also \cite{BO87}) and hence can be easily computed for many pairs $(G,O)$.
The Disjoint Divisors Theorem for Complete Varieties
2015 · PREPRINT · en
Given an infinite collection of pairwise-disjoint, Zariski-closed, connected, codimension-1 subvarieties of a complete, normal, irreducible algebraic variety over an algebraically-closed field, we prove that there exists a regular, nonconstant morphism to a complete curve so that each of these divisors is contained in a fiber of this morphism.
Rational curves on foliated varieties
2015 · CHAPTER · en
This article represents a study of ample subbundles of the tangent sheaf of a variety in a formal neighbourhood of a curve. With the added hypothesis of integrability it is best possible. A particular corollary is Mori’s cone theorem for foliations by curves.
Local structure of closed symmetric 2-differentials
2015 · CHAPTER · en
In the authors's previous work on symmetric differentials and their connection to the topological properties of the ambient manifold, a class of symmetric differentials was introduced: closed symmetric differentials ([BoDeO11] and [BoDeO13]). In this article we give a description of the local structure of closed symmetric 2-differentials on complex surfaces, with an emphasis towards the local decompositions as products of 1-differentials. We show that a closed symmetric 2-differential $w$ of rank 2 (i.e. defines two distinct foliations at the general point) has a subvariety $B_w\subset X$ outside of which $w$ is locally the product of closed holomorphic 1-differentials. The main result, theorem 2.6, gives a complete description of a (locally split) closed symmetric 2-differential in a neighborhood of a general point of $B_w$. A key feature of theorem 2.6 is that closed symmetric 2-differentials still have a decomposition as a product of 2 closed 1-differentials (in a generalized sense) even at the points of $B_w$. The (possibly multi-valued) closed 1-differentials can have essential singularities along $B_w$, but one still has a control on these essential singularities. The essential singularities come from exponentials of meromorphic functions acquiring poles along the irreducible components of $B_w$ of order bounded by the order of contact of the 2 foliations defined by the symmetric 2-differential along that irreducible component. Local structure of closed symmetric 2-differentials.
Stable cohomology of alternating groups
2014 · ARTICLE · en
We determine the stable cohomology groups H^i_s (A_n, Z/pZ) of the alternating groups A_n for all integers n and i, and all odd primes p.
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