Hermitian-Yang-Mills connections on some complete non-compact Kähler manifolds

2022/06/27 by Junsheng Zhang, Zhang, Junsheng
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.2206.13579

34 pages, all comments are welcome

arxiv created 2022/06/27 · arxiv updated 2022/06/29

Abstract

We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle E over some complete non-compact Kähler manifolds (X,ω), where X is the complement of a divisor in a compact Kähler manifold and we impose some conditions on the cohomology class and the asymptotic behaviour of the Kähler form ω. We introduce the notion of stability with respect to a pair of (1,1)-classes which generalizes the standard slope stability. We prove that this new stability condition is both sufficient and necessary for the existence of projectively Hermitian-Yang-Mills metrics in our setting.

Related

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• Continuity of HYM connections with respect to metric variations
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• Kobayashi-Hitchin correspondence for analytically stable bundles