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Local structure of singular hyperkahler quotients. (arXiv:1807.05992v1 [math.DG])
来源于:arXiv
When a compact Lie group acts freely and in a Hamiltonian way on a symplectic
manifold, the Marsden-Weinstein theorem says that the reduced space is a smooth
symplectic manifold. If we drop the freeness assumption, the reduced space
might be singular, but Sjamaar-Lerman (1991) showed that it can still be
partitioned into smooth symplectic manifolds which "fit together nicely" in the
sense that they form a stratification. In this paper, we prove a hyperkahler
analogue of this statement, using the hyperkahler quotient construction. We
also show that singular hyperkahler quotients are complex spaces which are
locally biholomorphic to affine complex-symplectic GIT quotients with
biholomorphisms that are compatible with natural holomorphic Poisson brackets
on both sides. 查看全文>>