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Harmonic bundles on quasi-compact Kaehler manifolds

Juergen Jost·Jiayu Li·Kang Zuo
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Abstract

We define the C^*-action on moduli spaces of reductive representations of fundamental groups of quasi-compact Kaehler manifolds by solving Hermitian-Yang-Mills equation. As applications in algebraic geometry we show a non-abelian Hodge (p,q)-type theorem for families of quasi-projective manifolds. We also prove that any discrete sub group of a Lie group of rank >1 that is not of Hodge type can't be the fundamental group of a quasi-compact Kaehler manifold.

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Juergen Jost, Jiayu Li, Kang Zuo. 2003-02-21. Harmonic bundles on quasi-compact Kaehler manifolds. https://arxiv.org/abs/math/0108166

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