Department Seminars & Colloquia

Category 학과 Seminar/ Colloquium
Event ASARC Seminar
Title A characterization of nilpotent varieties of complex semisimple Lie algebras II
Abstract

A complex normal variety $X$ is called a symplectic variety if it admits a holomorphic symplectic 2-form $omega$ on the regular part $X_{reg}$ and $omega$ extends to a holomorphic 2-form on a resolution $Y$ of $X$. Compared with the compact case, there are a lot of examples of affine symplectic varieties. They are not only interesting objects in algebraic geometry, but also play important roles in geometric representation theory.
The aim of this talk is to characterize the nilpotent variety of a complex semisimple Lie algebra among affine symplectic varieties. The main result is that if $(X, omega)$ is an affine singular symplectic variety embedded in an affine space as a complete  intersection of homogeneous polynomials and $omega$ is homogeneous, then $(X, omega)$ coincides with the nilpotent variety
$N$ of a complex semisimple Lie algebra together with the Kostant-Kirillov 2-form $omega_{KK}$.
The proof of the main result uses the theory of Poisson deformation, holomorphic contact geometry, Mori theory and some elementary  representation theory.

Daytime 2014-04-29 (Tue) / 17:00 ~ 18:00
Place 자연과학동(E6-1) Room 1409
Language English
Speaker`s name Yoshinori Namikawa
Speakers`s Affiliation Kyoto University
Speaker`s homepage
Other information
Hosts Prof.이용남
URL
담당자
연락처