On the Existence of Symplectic Resolutions of Symplectic Reductions

TL;DR

This paper investigates the existence of symplectic resolutions for specific symplectic reductions, providing explicit examples and descriptions, including cases with non-equivalent resolutions connected by flops.

Contribution

It computes symplectic reductions for certain group actions and offers explicit symplectic resolutions, including novel descriptions of non-equivalent resolutions.

Findings

Computed symplectic reductions for Sp_2n and Sl_2 actions.

Provided explicit symplectic resolutions where they exist.

Described non-equivalent resolutions connected by Mukai flops.

Abstract

We compute the symplectic reductions for the action of Sp_2n on several copies of C^2n and for all coregular representations of Sl_2. If it exists we give at least one symplectic resolution for each example. In the case Sl_2 acting on sl_2+C^2 we obtain an explicit description of Fu's and Namikawa's example of two non-equivalent symplectic resolutions connected by a Mukai flop.