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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Symplectic resolutions for Higgs moduli spaces
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by Andrea Tirelli PDF
Proc. Amer. Math. Soc. 147 (2019), 1399-1412 Request permission

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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Additional Information
  • Andrea Tirelli
  • Affiliation: Department of Mathematics, Imperial College, London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
  • Email: a.tirelli15@imperial.ac.uk
  • 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
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 1399-1412
  • MSC (2010): Primary 14B05, 14D20
  • DOI: https://doi.org/10.1090/proc/14339
  • MathSciNet review: 3910407