Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

Details Kobayashi-Hitchin correspondence for tame harmonic bundles and an application Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

2004-11-13

arxiv.org/abs/math/0411300v3

Mathematics

Differential Geometry

Scientific paper

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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