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arXiv · 2009.14680

An Analytic Approach to the Quasi-projectivity of the Moduli Space of Higgs Bundles

Yue Fan
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Abstract

The moduli space of Higgs bundles can be defined as a quotient of an infinite-dimensional space. Moreover, by the Kuranishi slice method, it is equipped with the structure of a normal complex space. In this paper, we will use analytic methods to show that the moduli space is quasi-projective. In fact, following Hausel's method, we will use the symplectic cut to construct a normal and projective compactification of the moduli space, and hence prove the quasi-projectivity. The main difference between this paper and Hausel's is that the smoothness of the moduli space is not assumed.

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Yue Fan. 2020-09-30. An Analytic Approach to the Quasi-projectivity of the Moduli Space of Higgs Bundles. https://arxiv.org/abs/2009.14680

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