On the spannedness of adjunction of vector bundles
type: Item
instance of: scholarly article
title: On the spannedness of adjunction of vector bundles
zbMATH Open document ID: 0909.14005
DOI: 10.1007/PL00004575
author: Qi Zhang
published in: Mathematische Zeitschrift
publication date: 1997-07-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174948
review text: Let \(X\) be a complex projective manifold of dimension \(n\) and \(E\) be an ample vector bundle on \(X\). The nefness and spannedness of the adjoint bundle \(K_X+c_1(E)\) has been investigated in several papers. Here the author asks for conditions ensuring that \(K_X+c_1(E)\) is spanned. \textit{M. C. Beltrametti, M. Schneider} and \textit{A. J. Sommese} [Math. Z. 214, No. 4, 593-600 (1993; Zbl 0804.14006)] had conjectured that, if \(E\) is of rank \(r\geq n\) and spanned, then the adjoint bundle is spanned unless \((X,E)\simeq ({\mathbb{P}}^n, \bigoplus^n{\mathcal O}_{{\mathbb{P}}^n}(1))\). The main result of this paper is an affirmative answer to this conjecture, under the additional condition that \(L\) is very ample, where \(L\) denotes the tautological line bundle on \(\text{Proj}_X(E)\), associated to \(E\).
reviewed by: Emilia Mezzetti
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 1028280
zbMATH Keywords: adjunction theory
zbMATH Keywords: adjoint bundle
zbMATH Keywords: spannedness
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1028280