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arXiv · 2004.05598

Holomorphic bundles trivializable by proper surjective holomorphic map

Indranil Biswas·Sorin Dumitrescu
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Abstract

Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $\varphi^* E$ is trivial for some surjective holomorphic map $\varphi$, to $M$, from some compact complex manifold. We prove that these are exactly those holomorphic vector bundles that admit a flat holomorphic connection with finite monodromy homomorphism. A similar result is proved for holomorphic principal $G$-bundles, where $G$ is a connected reductive complex affine algebraic group.

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Indranil Biswas, Sorin Dumitrescu. 2020-04-12. Holomorphic bundles trivializable by proper surjective holomorphic map. https://arxiv.org/abs/2004.05598

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