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Stratifications on the Moduli Space of Higgs Bundles

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arxiv 1511.03985 v4 pith:X3IPVHFT submitted 2015-11-12 math.AG

Peter B. Gothen , Ronald A. Zúñiga-Rojas This is my paper · ORCID
classification math.AG
keywords higgsbundlesmodulirankspacestratificationstratificationsbundle
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The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the Harder-Narasimhan type of the vector bundle underlying a Higgs bundle. While these two stratification coincide in the case of rank two Higgs bundles, this is not the case in higher rank. In this paper we analyze the relation between the two stratifications for the moduli space of rank three Higgs bundles.

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  1. Non-Abelian Hodge Theory and Related Topics

    math.AG 2019-08 conditional novelty 4.0 of 10

    A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.

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