Symplectic resolutions of character varieties

Abstract

In this article we consider the connected component of the identity of $G$-character varieties of compact Riemann surfaces of genus $g>0$, for connected complex reductive groups $G$ of type $A$ (e.g., $S{L}_n$ and $G{L}_n$). We show that these varieties are symplectic singularities and classify which admit symplectic resolutions. The classification reduces to the semi-simple case, where we show that a resolution exists if and only if either $g=1$ and $G$ is a product of special linear groups of any rank and copies of the group $PG{L}_2$, or if $g=2$ and $G=(S{L}_2{)}^m$ for some $m$.

arXiv commentIn this revised version, we extend results previously stated for GL or SL only to all reductive groups of type A

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Cited by in corpus (4)

• Multiplicative preprojective algebras are 2-Calabi-Yau
• Intersection cohomology of rank two character varieties of surface groups
• When does the zero fiber of the moment map have rational singularities?
• Crepant resolutions of stratified varieties via gluing