幾何学コロキウム Symplectic singularities

開催日時
2015年   6月 15日 15時 15分 ~ 2015年   6月 15日 16時 15分
場所
理学部3号館3-204
講演者
Wojciech Domitrz (Warsaw University of Technology, Poland)
 
We study germs of singular varieties in a symplectic space. We introduce the algebraic restrictions of differential forms to singular varieties and prove the generalization of Darboux-Givental’ theorem from smooth submanifolds to arbitrary quasi-homogeneous varieties in a symplectic space. Using algebraic restrictions we introduce new symplectic invariants and explain their geometric meaning. We show that a quasi-homogeneous variety N is contained in a non-singular Lagrangian submanifold if and only if the algebraic restriction of the symplectic form to N vanishes. The method of algebraic restriction is a powerful tool for various classification problems in a symplectic space. We illustrate this by the construction of a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.

関連項目

研究集会・セミナー・集中講義の一覧へ