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arXiv · 1903.07247

On the complex structure of symplectic quotients

Xiangsheng Wang
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Abstract

Let $K$ be a compact group. For a symplectic quotient $M_{\lambda}$ of a compact Hamiltonian K\"ahler $K$-manifold, we show that the induced complex structure on $M_{\lambda}$ is locally invariant when the parameter $\lambda$ varies in $\mathrm{Lie}(K)^*$. To prove such a result, we take two different approaches: (i) by using the complex geometry properties of the symplectic implosion construction; (ii) by investigating the variation of GIT quotients.

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Xiangsheng Wang. 2019-03-18. On the complex structure of symplectic quotients. https://doi.org/10.1007/s11425-019-1783-6

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