Positivity of Singular Hermitian Metrics for Holomorphic Vector Bundles

Fuente: arXiv
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Autore principale: Varolin, Dror
Natura: Preprint
Pubblicazione: 2023
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author Varolin, Dror
author_facet Varolin, Dror
contents We introduce a notion of Nakano and Demailly positivity for singular Hermitian metrics of holomorphic vector bundles. Our definitions support the usual Hörmander and Nadel type vanishing theorems with estimates, at least on essentially Stein manifolds. As an application, we establish a sharp Ohsawa-Takegoshi type $L^2$ extension theorem. We use the method of Berndtsson and Lempert to prove the latter theorem, and for this purpose we require a Berndtsson-type positivity theorem for holomorphic vector bundles, which we also prove.
format Preprint
id arxiv_https___arxiv_org_abs_2308_13364
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Positivity of Singular Hermitian Metrics for Holomorphic Vector Bundles
Varolin, Dror
Complex Variables
Differential Geometry
32, 53
We introduce a notion of Nakano and Demailly positivity for singular Hermitian metrics of holomorphic vector bundles. Our definitions support the usual Hörmander and Nadel type vanishing theorems with estimates, at least on essentially Stein manifolds. As an application, we establish a sharp Ohsawa-Takegoshi type $L^2$ extension theorem. We use the method of Berndtsson and Lempert to prove the latter theorem, and for this purpose we require a Berndtsson-type positivity theorem for holomorphic vector bundles, which we also prove.
title Positivity of Singular Hermitian Metrics for Holomorphic Vector Bundles
topic Complex Variables
Differential Geometry
32, 53
url https://arxiv.org/abs/2308.13364