## Symplectic resolutions for Higgs moduli spaces

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- by Andrea Tirelli PDF
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**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.## References

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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