Applications of the Ein-Lazarsfeld criterion for spannedness of adjoint bundles
type: Item
instance of: scholarly article
title: Applications of the Ein-Lazarsfeld criterion for spannedness of adjoint bundles
zbMATH Open document ID: 0804.14006
DOI: 10.1007/BF02572427
author: Mauro C. Beltrametti
author: Michael Schneider
author: Andrew J. Sommese
published in: Mathematische Zeitschrift
publication date: 1995-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/174589
review text: In this paper using Ein-Lazarsfeld's criteria for the spannedness of the adjoint bundle \(K_ X \otimes L\), of a nef and big line bundle, \(L\), on a complex projective 3-fold \(X\) and some inequalities for the Chern classes of ample and spanned vector bundles given by the authors in \S1, they prove: If \(E\) is an ample and spanned vector bundle on a smooth 3-fold \(X\) then \(K_ X \otimes \text{det} (E)\) is spanned if \(\text{rank} (E) \geq 3\) and \(L^ 3 \geq 850\) or if \(\text{rank} (E) \geq 4\) and \(L^ 3 \geq 162\) or if \(\text{rank} (E) \geq 13\). In the last section, using again Ein-Lazarsfeld's criteria the authors study projective \(n\)-folds without rational curves.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14J60
zbMATH DE Number: 567429
zbMATH Keywords: \(n\)-folds without rational curves
zbMATH Keywords: spannedness of the adjoint bundle
reviewed by: Rosa M. Miró-Roig
MaRDI profile type: Publication
cites work: Global Generation of Pluricanonical and Adjoint Linear Series on Smooth Projective Threefolds
cites work: Q4027239
cites work: Q3328651
cites work: Ample Vector Bundles on Curves
cites work: Q4019738
cites work: A vector bundle characterization of \({\mathbb{P}}^ n\)
cites work: Stable and unitary vector bundles on a compact Riemann surface
cites work: Vector bundles of rank 2 and linear systems on algebraic surfaces
cites work: On the degree of the Gauss mapping of a submanifold of an Abelian variety
cites work: Length of extremal rays and generalized adjunction
cites work: On ample vector bundles whose adjunction bundles are not numerically effective
description: scientific article; zbMATH DE number 567429