Polystable bundles and representations of their automorphisms

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2022-01-01 DOI:10.1515/coma-2021-0131

N. Buchdahl, G. Schumacher

引用次数: 3

Abstract

Abstract 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.

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多稳定丛及其自同构的表示

摘要利用Hodge理论的准线性版本，证明了紧致Kähler流形上给定多稳态丛邻域中的全纯向量丛是（poly）稳定的，当且仅当它们对应的类在几何不变量理论意义上关于丛的自同构群在其in-nitesimal变形空间上的线性作用是（poly）稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.