NDLI: Symplectic quotients have symplectic singularities

Content Provider	Scilit
Author	Herbig, Hans-Christian Schwarz, Gerald W. Seaton, Christopher
Copyright Year	2020
Description	Journal: Compositio Mathematica Let $K$ be a compact Lie group with complexification $G$, and let $V$ be a unitary $K$-module. We consider the real symplectic quotient $M_{0}$ at level zero of the homogeneous quadratic moment map as well as the complex symplectic quotient, defined here as the complexification of $M_{0}$. We show that if $(V,G)$ is $3$-large, a condition that holds generically, then the complex symplectic quotient has symplectic singularities and is graded Gorenstein. This implies in particular that the real symplectic quotient is graded Gorenstein. In case $K$ is a torus or $\operatorname{SU}_{2}$, we show that these results hold without the hypothesis that $(V,G)$ is $3$-large.
Ending Page	646
Starting Page	613
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x19007784
Journal	Compositio Mathematica
Issue Number	3
Volume Number	156
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2020-01-31
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics Symplectic Quotient Symplectic Singularities
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Symplectic quotients have symplectic singularities