Generically surjective morphisms of holomorphic vector bundles via degenerations

Roberto Albesiano

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arXiv · 2503.01059

Generically surjective morphisms of holomorphic vector bundles via degenerations

Roberto Albesiano

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Abstract

We prove an $L^2$ theorem on generically surjective morphism of holomorphic vector bundles via a degeneration argument, generalizing the author's previous work on the $L^2$ division theorem of Skoda. The proof is based on Berndtsson's theorem on the positivity of direct image bundles and is inspired by Berndtsson and Lempert's proof of the $L^2$ extension theorem.

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Roberto Albesiano. 2025-03-02. Generically surjective morphisms of holomorphic vector bundles via degenerations. https://arxiv.org/abs/2503.01059

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