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HOLOMORPHIC BUNDLES TRIVIALIZABLE BY PROPER SURJECTIVE HOLOMORPHIC MAP

Abstract : Given a compact complex manifold M , we investigate the holomorphic vector bundles E on M such that ϕ * E is trivial for some surjective holomorphic map ϕ, 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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Submitted on : Sunday, April 12, 2020 - 2:53:10 PM
Last modification on : Wednesday, March 16, 2022 - 3:46:35 AM

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Indranil Biswas, Sorin Dumitrescu. HOLOMORPHIC BUNDLES TRIVIALIZABLE BY PROPER SURJECTIVE HOLOMORPHIC MAP. International Mathematics Research Notices, Oxford University Press (OUP), inPress, 2022 (5), pp.3636-3650. ⟨hal-02540982⟩

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