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arXiv · 2002.03548

Polystability and the Hitchin-Kobayashi correspondence

Nicholas Buchdahl·Georg Schumacher
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Abstract

Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kaehler manifold are shown to be (poly)stable if and only if their corresponding classes are (poly)stable in the sense of geometric invariant theory with respect to the linear action of the automorphism group of the bundle on its space of infinitesimal deformations.

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Nicholas Buchdahl, Georg Schumacher. 2020-02-10. Polystability and the Hitchin-Kobayashi correspondence. https://arxiv.org/abs/2002.03548

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