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Symplectic resolutions for Higgs moduli spaces

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arxiv 1701.07468 v1 pith:YRO4TFDH submitted 2017-01-25 math.AG math.SG

Andrea Tirelli This is my paper · ORCID
classification math.AGmath.SG
keywords symplecticmodulispaceshiggsadmitalgebraicapplicationbea00
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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 [Bea00], 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 [BS16] via the so-called Isosingularity Theorem.

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