Kobayashi-Hitchin correspondence for tame harmonic bundles II

Abstract

Let $X$ be a smooth projective complex variety with an ample line bundle $L$, and let $D$ be a simple normal crossing divisor. We establish the Kobayashi-Hitchin correspondence between tame harmonic bundles on $X-D$ and ${\mu }_L$-stable parabolic $\lambda$-flat bundles with trivial characteristic numbers on $(X,D)$. Especially, we obtain the quasiprojective version of the Corlette-Simpson correspondence between flat bundles and Higgs bundles.

Some arguments are simplified

References in corpus (4)

• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules
• Wild Harmonic Bundles and Wild Pure Twistor D-modules
• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
• Polarizable twistor D-modules

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• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
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• Introduction to Nonabelian Hodge Theory: flat connections, Higgs bundles and complex variations of Hodge structure
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• Non-Abelian Hodge Theory and Related Topics
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• Cohomology jump loci of quasi-projective varieties
• Kobayashi-Hitchin correspondence for analytically stable bundles
• Semi-stable Higgs sheaves and Bogomolov type inequality
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• The Kapustin-Witten equations and nonabelian Hodge theory
• Vanishing theorem for tame harmonic bundles via $L^2$-cohomology
• Parabolic log convergent isocrystals
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• Generalized Deligne-Hitchin Twistor Spaces: Construction and Properties
• Moduli spaces of parabolic bundles over ${\mathbb{P}}^1$ with five marked points
• Vanishing theorems for parabolic Higgs bundles
• The limit of the Hermitian-Yang-Mills flow on reflexive sheaves
• Poisson metrics and Higgs bundles over noncompact Kähler manifolds
• Generalized Donaldson's functionals and related nonlinear partial differential equations
• Analytically stable Higgs bundles on some non-Kähler manifolds