Remarks on Seshadri constants of vector bundles
type: Item
instance of: scholarly article
title: Remarks on Seshadri constants of vector bundles
zbMATH Open document ID: 0956.14034
publication date: 2000-07-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75437
review text: Let \(X\) be a smooth complex projective variety and \(P\in X\). Here the author introduces the notion of Seshadri constant \(\varepsilon(E,P)\) of an ample vector bundle \(E\) on \(X\) at \(P\), generalizing the case \(\text{rank} (E)=1\) which produced a huge number of nice results. The generalization is successful because the author proves here a theorem which states that \(\varepsilon (E,P)\geq 1\) for \(P\) outside countably many proper subvarieties of \(X\) under assumptions which are natural, but too technical to be stated here. As an application he gives conditions for the spannedness of \(\omega_X\otimes S^t(E) \otimes \det(E)\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 1478803
zbMATH Keywords: Seshadri constants
zbMATH Keywords: ample vector bundles
zbMATH Keywords: spanned vector bndles
zbMATH Keywords: stability of vector bundles
author: Christopher Hacon
MaRDI profile type: Publication
OpenAlex ID: W2320552582
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DOI: 10.5802/AIF.1772
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published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1478803