Polystability and the Hitchin-Kobayashi correspondence
Differential Geometry
2020-02-11 v1
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.
Cite
@article{arxiv.2002.03548,
title = {Polystability and the Hitchin-Kobayashi correspondence},
author = {Nicholas Buchdahl and Georg Schumacher},
journal= {arXiv preprint arXiv:2002.03548},
year = {2020}
}