On the complex structure of symplectic quotients

Abstract

Let $K$ be a compact group. For a symplectic quotient $M_{\lambda }$ of a compact Hamiltonian Kähler $K$-manifold, we show that the induced complex structure on $M_{\lambda }$ is locally invariant when the parameter $\lambda$ varies in $\mathrm{Lie}(K{)}^{\ast }$. 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.

29 pages, fixing some typos, final

References in corpus (1)

• Symplectic implosion and the Grothendieck-Springer resolution