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The Orbit Type Stratification OF the Moduli Space of Higgs Bundles

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arxiv 2005.13649 v1 pith:TVJ6LRUU submitted 2020-05-27 math.DG math.AG

The Orbit Type Stratification OF the Moduli Space of Higgs Bundles

classification math.DG math.AG
keywords spacecomplexmoduliorbitpoissontypeadmitsbracket
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The moduli space of Higgs bundles can be constructed as a quotient of an infinite-dimensional space and hence admits an orbit type decomposition. In this paper, we show that the orbit type decomposition is a complex Whitney stratification such that each stratum is a complex symplectic submanifold and hence admits a complex Poisson bracket. Moreover, these Poisson brackets glue to a Poisson bracket on the structure sheaf of the moduli space so that the moduli space is a stratified complex symplectic space

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