Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

By T. Mochizuki. Astérisque, 2004

136 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6a112d1ec9e5e2ab9dd7a88929d2cf9683a43725

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces (2015, methodology): “We recall the following proposition, for which a proof was given in [14], for example.”
Local Systems on Proper Algebraic V -manifolds (2010, background): “If L• is the pullback of a local system LZ , then it is also the pullback of the associated-graded of the Jordan-Hölder series for LZ , so we may assume LZ semisimple; it then has a harmonic metric [71] which restricts to a strong polarization of L•.”
The Miyaoka-Yau inequality and uniformisation of canonical models (2015, methodology): “ currently working towards removing this additional assumption by comparing the Nonabelian Hodge correspondence on a resolution of a given klt variety Xto Mochizuki’s Nonabelian Hodge correspondence, [Moc06], on the smooth part ofX. AnalternativeapproachconsistsinprovingthatageneralisationoftheNonab”