Symplectic quotients have symplectic singularities
2020 ◽
Vol 156
(3)
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pp. 613-646
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Keyword(s):
The Real
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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.
2013 ◽
Vol 15
(03)
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pp. 1250056
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Keyword(s):
1982 ◽
Vol s2-26
(3)
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pp. 557-566
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Keyword(s):
1977 ◽
Vol 16
(2)
◽
pp. 279-295
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Keyword(s):
2009 ◽
Vol 61
(3)
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pp. 921-969