Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Symplectic resolutions for Higgs moduli spaces


Author: Andrea Tirelli
Journal: Proc. Amer. Math. Soc. 147 (2019), 1399-1412
MSC (2010): Primary 14B05, 14D20
DOI: https://doi.org/10.1090/proc/14339
Published electronically: December 12, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14B05, 14D20

Retrieve articles in all journals with MSC (2010): 14B05, 14D20


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

DOI: https://doi.org/10.1090/proc/14339
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