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Symplectic resolutions of character varieties

Gwyn Bellamy and Travis Schedler

Geometry & Topology 27 (2023) 51–86
Abstract

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 (eg SL n and GL n). We show that these varieties are –factorial symplectic singularities and classify which admit symplectic resolutions. The classification reduces to the semisimple 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 PGL 2, or g = 2 and G = (SL 2)m for some m.

Keywords
symplectic resolution, character variety, Poisson variety
Mathematical Subject Classification 2010
Primary: 14D20, 16D20
Secondary: 16S80, 17B63
References
Publication
Received: 26 September 2019
Revised: 10 July 2021
Accepted: 15 August 2021
Published: 1 May 2023
Proposed: Ciprian Manolescu
Seconded: Frances Kirwan, Richard P Thomas
Authors
Gwyn Bellamy
School of Mathematics and Statistics
University of Glasgow
Glasgow
United Kingdom
Travis Schedler
Department of Mathematics
Imperial College London
London
United Kingdom

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