When does the zero fiber of the moment map have rational singularities?

Hans-Christian Herbig, Gerald W. Schwarz, Christopher Seaton

Let $G$ be a complex reductive group and $V$ a $G$-module. There is a natural moment mapping $\mu :V\oplus V^{\ast }\to {\mathfrak{g}}^{\ast }$ and we denote ${\mu }^{-1}(0)$ (the shell) by $N_V$.…