Hermitian-Yang-Mills connections on some complete non-compact K\"ahler manifolds

Junsheng Zhang

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arXiv · 2206.13579

Hermitian-Yang-Mills connections on some complete non-compact K\"ahler manifolds

Junsheng Zhang

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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 K\"ahler manifolds $(X,\omega)$, where $X$ is the complement of a divisor in a compact K\"ahler manifold and we impose some conditions on the cohomology class and the asymptotic behaviour of the K\"ahler form $\omega$. 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.

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Junsheng Zhang. 2022-06-27. Hermitian-Yang-Mills connections on some complete non-compact K\"ahler manifolds. https://arxiv.org/abs/2206.13579

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