Fedor Bogomolov

Fyodor Alexeyevich Bogomolov (Russian Фёдор Алексеевич Богомолов; Fedor Alekseevich Bogomolov English transcription; born September 26, 1946 in Moscow ) is a Russian- American mathematician who deals with algebraic geometry.

Bogomolov studied at the Moscow State University and received his PhD in 1973 (Candidate items) at the Steklov Institute in Sergei Novikov ( Compact Kähler manifolds ). In 1983 he completed his habilitation (Russian doctorate ). In 1994 he went to the USA and became a professor at the Courant Institute of Mathematical Sciences of New York University.

Bogomolov studied in his early works and Hyperkähler Kähler manifolds ( Riemannian manifolds with symplectic group as holonomy group ). Bogomolov she examined as a complex algebraic varieties ( holomorphic symplectic manifolds ) and gave for this in a 1974 named after him decomposition theorem criteria for that the holonomy group of compact holomorphic symplectic manifolds is symplectic. Later he studied the deformation theory of Hyperkähler -manifolds, which led to the Bogomolov - Tian- Todorov theorem ( from the particular followed that the deformations of Calabi -Yau manifolds no obstructions had ). This work forms one of the foundations of the studied in string theory mirror symmetry

In 1978 he studied holomorphic vector bundles in projective space (where he introduced Bogomolov stability of vector bundles ) and demonstrated a after him, Shing-Tung Yau and Yoichi Miyaoka inequality named for the Chernzahlen compact complex surfaces.

In 1977 he proved that it was on algebraic surfaces general type whose Chernzahlen satisfy the inequality, only a finite number of curves with limited Gender exist .. The work for the later development of hyperbolic arithmetic algebraic geometry important (Paul Vojta, Serge Lang) and was extended by Michael McQuillan in his proof of the conjecture of Green and Griffiths.

In 1976 he published a work on the still open problem of the classification of algebraic surfaces of Kodaira class VII.

After Bogomolov even a guess in Diophantine geometry is named, which generalizes the Manin - Mumford conjecture and was proved by Emmanuel Ullmo 1998.

In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Unstable vector bundles and curves on surfaces ).

Writings

• With Yuri Tschinkel (Editor): Cohomological and geometric approaches to rationality problems - new perspectives, Birkhäuser, Progress in Mathematics 2009