On the complex structure of symplectic quotients

被引：0
|
作者：
Xiangsheng Wang
机构：
[1] Beijing International Center for Mathematical Research, Peking University
[2] School of Mathematics, Shandong University
来源：
ScienceChina(Mathematics) | 2021年 / 64卷 / 12期
基金：
中国博士后科学基金;
关键词：
D O I：
暂无
中图分类号：
O186.1 [微分几何];
学科分类号：
0701 ; 070101 ;
摘要：
Let K be a compact group. For a symplectic quotient Mof a compact Hamiltonian K?hler Kmanifold, we show that the induced complex structure on Mis locally invariant when the parameter λ varies in Lie(K)~*. To prove such a result, we take two different approaches:(i) use the complex geometry properties of the symplectic implosion construction;(ii) investigate the variation of geometric invariant theory(GIT) quotients.
引用
收藏
页码：2719 / 2742
页数：24
相关论文
共 50 条
  • [1] On the complex structure of symplectic quotients
    Xiangsheng Wang
    Science China Mathematics, 2021, 64 : 2719 - 2742
  • [2] On the complex structure of symplectic quotients
    Wang, Xiangsheng
    SCIENCE CHINA-MATHEMATICS, 2021, 64 (12) : 2719 - 2742
  • [3] The topological structure of contact and symplectic quotients
    Lerman, E
    Willett, C
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2001, 2001 (01) : 33 - 52
  • [4] Pushing down the Rumin complex to conformally symplectic quotients
    Cap, Andreas
    Salac, Tomas
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2014, 35 : 255 - 265
  • [5] Symplectic quotients have symplectic singularities
    Herbig, Hans-Christian
    Schwarz, Gerald W.
    Seaton, Christopher
    COMPOSITIO MATHEMATICA, 2020, 156 (03) : 613 - 646
  • [6] Symplectic implosion and nonreductive quotients
    Kirwan, Frances
    GEOMETRIC ASPECTS OF ANALYSIS AND MECHANICS: IN HONOR OF THE 65TH BIRTHDAY OF HANS DUISTERMAAT, 2011, 292 : 213 - 256
  • [7] COHOMOLOGY RINGS OF SYMPLECTIC QUOTIENTS
    KALKMAN, J
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1995, 458 : 37 - 52
  • [8] The cohomology rings of symplectic quotients
    Tolman, S
    Weitsman, J
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2003, 11 (04) : 751 - 773
  • [9] Complex Ball Quotients and New Symplectic 4-manifolds with Nonnegative Signatures
    Akhmedov, Anar
    Sakalli, Sumeyra
    Yeung, Sai-Kee
    TAIWANESE JOURNAL OF MATHEMATICS, 2024, 28 (01): : 29 - 53
  • [10] Algebraic symplectic analogues of additive quotients
    Doran, Brent
    Hoskins, Victoria
    JOURNAL OF SYMPLECTIC GEOMETRY, 2018, 16 (06) : 1591 - 1638
12345