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Symplectic resolutions for Higgs moduli spaces

Author: Andrea Tirelli
Journal: Proc. Amer. Math. Soc. 147 (2019), 1399-1412
MSC (2010): Primary 14B05, 14D20
Published electronically: December 12, 2018
MathSciNet review: 3910407
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Abstract: In this paper, we study the algebraic symplectic geometry of the singular moduli spaces of Higgs bundles of degree $0$ and rank $n$ on a compact Riemann surface $X$ of genus $g$. In particular, we prove that such moduli spaces are symplectic singularities, in the sense of Beauville [Invent. Math. 139 (2000), 541–549], and admit a projective symplectic resolution if and only if $g=1$ or $(g, n)=(2,2)$. These results are an application of a recent paper by Bellamy and Schedler [ArXiv e-print (2016)] via the so-called Isosingularity Theorem.

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Andrea Tirelli
Affiliation: Department of Mathematics, Imperial College, London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom

Received by editor(s): February 16, 2017
Received by editor(s) in revised form: July 19, 2018
Published electronically: December 12, 2018
Additional Notes: This work was supported by the Engineering and Physical Sciences Research Council [EP/L015234/1], The EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), Imperial College London, and University College London.
Communicated by: Michael Wolf
Article copyright: © Copyright 2018 American Mathematical Society