Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

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.

Cited by in corpus (17)

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• Direct Images in Non Abelian Hodge Theory
• Regulators of canonical extensions are torsion: the smooth divisor case
• The Kapustin-Witten equations and nonabelian Hodge theory
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• Canonical Heights on Shimura Varieties and the André-Oort Conjecture
• Hyperkähler metrics on the moduli space of weakly parabolic Higgs bundles
• Generalized Donaldson's functionals and related nonlinear partial differential equations
• Poisson metrics and Higgs bundles over noncompact Kähler manifolds
• A note on curvature estimate of the Hermitian-Yang-Mills flow
• The Chern character of a parabolic bundle, and a parabolic Reznikov theorem in the case of finite order at infinity
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