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Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

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arxiv math/0411300 v3 pith:UIE5B7CA submitted 2004-11-13 math.DG math.AGmath.GT

Takuro Mochizuki This is my paper · ORCID
classification math.DGmath.AGmath.GT
keywords bundlescorrespondenceharmonichiggsparabolicprojectivequasismooth
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abstract

We establish the correspondence between tame harmonic bundles and $\mu_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $\mu_L$-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deformed to a variation of polarized Hodge structure. As a consequence, we can conclude that some kind of discrete groups cannot be a split quotient of the fundamental group of a smooth quasi projective variety.

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  1. Logarithmic Non-Abelian Hodge Theory for curves in prime characteristic

    math.AG 2025-01 conditional novelty 7.0 of 10

    A logarithmic version of the characteristic-p Non-Abelian Hodge theorem, over an Artin-Schreier cover of the Hitchin base, with semistable and GL_r cohomological applications.

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