Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

2004/11/13 by Takuro Mochizuki, Mochizuki, Takuro · 10 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.math/0411300

Abstract

We establish the correspondence between tame harmonic bundles and μ_L-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for μ_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

• Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories
• The Chern Invariants for Parabolic Bundles at Multiple Points
• Kobayashi-Hitchin correspondence for analytically stable bundles
• Geometric Endoscopy and Mirror Symmetry
• Moduli spaces of parabolic bundles over ℙ¹ with five marked points
• A note on curvature estimate of the Hermitian-Yang-Mills flow
• Regulators of canonical extensions are torsion: the smooth divisor case
• Semi-positivity from Higgs bundles
• Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds
• A report on "Regulators of canonical extension are torsion; the smooth divisor case"

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