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BY 4.0 license Open Access Published by De Gruyter Open Access March 12, 2022

Polystable bundles and representations of their automorphisms

  • Nicholas Buchdahl EMAIL logo and Georg Schumacher
From the journal Complex Manifolds


Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kähler 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 in˝nitesimal deformations.

MSC 2010: 53C07; 14L24; 32G13; 32L10; 32Q15


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Received: 2021-07-31
Revised: 2021-12-22
Accepted: 2022-02-02
Published Online: 2022-03-12

© 2022 Nicholas Buchdahl et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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