On the existence of symplectic resolutions of symplectic reductions

Abstract

We compute the symplectic reductions for the action of Sp2n on several copies of \({\mathbb{C}^{2n}}\) and for all coregular representations of Sl2. If it exists we give at least one symplectic resolution for each example. In the case Sl2 acting on \({\mathfrak{sl}_2 \oplus \mathbb{C}^2}\) we obtain an explicit description of Fu’s and Namikawa’s example of two non-equivalent symplectic resolutions connected by a Mukai flop (Fu and Namikawa in Ann Inst Fourier, Grenoble 54(1):1–19, 2004).