|
Fedor Alekseyevich Bogomolov (born 26 September 1946) (Фёдор Алексеевич Богомолов) is a Russian and American mathematician, known for his research in algebraic geometry and number theory. Bogomolov worked at Steklov Institute in Moscow before he became a professor at Courant Institute. He is most famous for his pioneering work on hyperkähler manifolds. Born in Moscow, Bogomolov graduated from Moscow State University, Faculty of Mechanics and Mathematics, and earned his doctorate (''"candidate degree"'') in 1973, in Steklov Institute. His advisor was Sergei Novikov. == Geometry of Kähler manifolds == Bogomolov's Ph. D. was entitled ''Compact Kähler varieties''. In his early papers〔Bogomolov, F. A. ''Manifolds with trivial canonical class.'' (Russian) Uspehi Mat. Nauk 28 (1973), no. 6 (174), 193–194. 〕〔Bogomolov, F. A. ''Kähler manifolds with trivial canonical class''. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 11–21 〕〔Bogomolov, F. A. ''The decomposition of Kähler manifolds with a trivial canonical class.'' (Russian) Mat. Sb. (N.S.) 93(135) (1974), 573–575, 630. 〕 Bogomolov studied the manifolds which were later called Calabi–Yau and hyperkaehler. He proved a decomposition theorem, used for the classification of manifolds with trivial canonical class. It has been re-proven using the Calabi–Yau theorem and Berger's classification of Riemannian holonomies, and is foundational for modern string theory. In the late 1970s and early 1980s Bogomolov studied the deformation theory for manifolds with trivial canonical class.〔Bogomolov, F. A., ''Kähler manifolds with trivial canonical class,'' Preprint Institute des Hautes Etudes Scientifiques 1981 pp. 1–32.〕 He discovered what is now known as Bogomolov–Tian–Todorov theorem, proving the smoothness and un-obstructedness of the deformation space for hyperkaehler manifolds (in 1978 paper) and then extended this to all Calabi–Yau manifolds in the 1981 IHES preprint. Some years later, this theorem became the mathematical foundation for Mirror Symmetry. While studying the deformation theory of hyperkaehler manifolds, Bogomolov discovered what is now known as Bogomolov–Beauville–Fujiki form on . Studying properties of this form, Bogomolov erroneously concluded that compact hyperkaehler manifolds don't exist, with exception of a K3 surface, torus and their products. Almost four years passed since this publication before Fujiki found a counterexample. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fedor Bogomolov」の詳細全文を読む スポンサード リンク
|