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 (36)

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• Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces
• Polyhedral Kahler Manifolds
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• Geometric Endoscopy and Mirror Symmetry
• Foliations on the moduli space of rank two connections on the projective line minus four points
• Semi-positivity from Higgs bundles
• Higgs bundles over non-compact Gauduchon manifolds
• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
• Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature
• Rank 3 rigid representations of projective fundamental groups
• Introduction to Nonabelian Hodge Theory: flat connections, Higgs bundles and complex variations of Hodge structure
• Doubly periodic monopoles and $q$-difference modules
• Direct Images in Non Abelian Hodge Theory
• Non-Abelian Hodge Theory and Related Topics
• Regulators of canonical extensions are torsion: the smooth divisor case
• Kobayashi-Hitchin correspondence for analytically stable bundles
• Semi-stable Higgs sheaves and Bogomolov type inequality
• The limit of the Yang-Mills-Higgs flow on Higgs bundles
• Canonical Heights on Shimura Varieties and the André-Oort Conjecture
• The Kapustin-Witten equations and nonabelian Hodge theory
• Parabolic log convergent isocrystals
• Fourier-Mukai transformation and logarithmic Higgs bundles on punctual Hilbert schemes
• Hyperkähler metrics on the moduli space of weakly parabolic Higgs bundles
• Vanishing and injectivity for R-Hodge modules and R-divisors
• The limit of the Hermitian-Yang-Mills flow on reflexive sheaves
• Vanishing theorems for parabolic Higgs bundles
• Moduli of parabolic sheaves on a polarized logarithmic scheme
• A report on "Regulators of canonical extension are torsion; the smooth divisor case"
• Poisson metrics and Higgs bundles over noncompact Kähler manifolds
• The Chern Invariants for Parabolic Bundles at Multiple Points
• Generalized Donaldson's functionals and related nonlinear partial differential equations
• Analytically stable Higgs bundles on some non-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