About

Fedor Bogomolov is a Silver Professor of Mathematics at NYU, with research interests in algebraic geometry and related problems in algebra, topology, and number theory. His work focuses on deep mathematical structures and their interconnections, contributing to the understanding of complex geometric and algebraic systems. As a prominent figure in his field, he has advanced the theoretical foundations of algebraic geometry, impacting related areas in mathematics.

Research topics

• Computer Science
• Mathematics
• Physics
• Pure mathematics
• Mathematical analysis
• Materials science
• Geometry

Selected publications

• Stabilization of direct images for curves

  ArXiv.org · 2025-01-31

  preprintOpen access1st authorCorresponding

  We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.

  PublisherOA PDFDOI

• Sections of Lagrangian fibrations on holomorphic symplectic manifolds

  arXiv (Cornell University) · 2024-07-10

  preprintOpen access1st authorCorresponding

  Let $M$ be a holomorphically symplectic manifold, equipped with a Lagrangian fibration $π:\; M \to X$. A degenerate twistor deformation (sometimes also called ``a Tate-Shafarevich twist'') is a family of holomorphically symplectic structures on $M$ parametrized by $H^{1,1}(X)$. All members of this family are equipped with a holomorphic Lagrangian projection to $X$, and their fibers are isomorphic to the fibers of $π$. Assume that $M$ is a compact hyperkahler manifold of maximal holonomy, and the general fiber of the Lagrangian projection $π$ is primitive (that is, not divisible) in integer homology. We also assume that $π$ has reduced fibers in codimension 1. Then $M$ has a degenerate twistor deformation $M'$ such that the Lagrangian projection $π:\; M' \to X$ admits a meromorphic section.

  PublisherOA PDFDOI

• Алексей Николаевич Паршин (некролог)

  Успехи математических наук · 2023-01-01

  articleOpen access1st authorCorresponding

  Алексей Николаевич Паршин18 июня 2022 г. ушел из жизни выдающийся советский и российский математик, ярчайший представитель московской

  PublisherOA PDFDOI

• Memorial Article for Yuri Manin

  Notices of the American Mathematical Society · 2023

  1st authorCorresponding
  • Computer Science
  • Computer Science

  Yuri Manin was

  PublisherDOI

• Alexey Nikolaevich Parshin (obituary)

  Russian Mathematical Surveys · 2023-01-01

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Viktor Stepanovich Kulikov (on his 70th birthday)

  Russian Mathematical Surveys · 2022-01-01

  article1st authorCorresponding
  PublisherDOI

• Stable vector bundles on the families of curves

  European Journal of Mathematics · 2022-02-14

  articleOpen access1st author

  Abstract We offer a new approach to proving the Chen–Donaldson–Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a family of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.

  PublisherOA PDFDOI

• Sections of Lagrangian fibrations on holomorphically symplectic manifolds and degenerate twistorial deformations

  Advances in Mathematics · 2022 · 8 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Mathematical analysis
  PublisherOA PDFDOI

• Виктор Степанович Куликов (к семидесятилетию со дня рождения)

  Успехи математических наук · 2022-01-01

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• On Stable Cohomology of Central Extensions of Elementary Abelian Groups

  Cambridge University Press eBooks · 2022-09-30

  book-chapter1st authorCorresponding

  We consider that kernels of inflation maps associated with extraspecial p-groups in stable group cohomology are generated by their degree-2 components. This turns out to be true if the prime is large enough compared to the rank of the elementary abelian quotient, but false in general.

  PublisherDOI

Recent grants

• Algebraic varieties, birational geometry and the structure of the Galois groups

  NSF · $208k · 2007–2010

• Algebraic Varieties, Birational Geometry and the Structure of the Galois Groups

  NSF · $135k · 2004–2007

• Algebraic Varieties, Birational Geometry and the Structure of the Galois Groups

  NSF · $149k · 2010–2013

Frequent coauthors

• Yuri Tschinkel

  New York University

  75 shared

• Tihomir Petrov

  California State University System

  47 shared

• Bruno De Oliveira

  26 shared

• Christian Böhning

  University of Warwick

  24 shared

• Виктор Степанович Куликов

  24 shared

• Алексей Николаевич Паршин

  23 shared

• Ivan Cheltsov

  23 shared

• Misha Verbitsky

  Mersen (France)

  22 shared

Education

• Ph.D., Mathematics

  Steklov Institute of Mathematics

  1974

• Other, Mathematics

  Moscow University

  1970