Symplectic quotients have symplectic singularities

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 sho...

Full description

Saved in:
Bibliographic Details
Published in:Compositio mathematica 2020-03, Vol.156 (3), p.613-646
Main Authors: Herbig, Hans-Christian, Schwarz, Gerald W., Seaton, Christopher
Format: Article
Language:English
Subjects:
Lie groups
Quotients
Singularity (mathematics)
Toruses
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X19007784