On 2-spannedness for the adjunction mapping
type: Item
instance of: scholarly article
title: On 2-spannedness for the adjunction mapping
zbMATH Open document ID: 0661.14005
DOI: 10.1007/BF01258599
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155325
review text: Let X be a smooth, complete variety of dimension greater than or equal to 1. An (effective) 0-cycle \(Z\subset X\) is called curvilinear, if \(Z\subset C\subset X\), where C is a smooth projective curve. A line bundle L on X is k-spanned if for all curvilinear cycles \(Z\subset C\), with \(\ell ({\mathcal O}_ Z)=k+1\), the natural map \(H^ 0(L)\to H^ 0(L\otimes {\mathcal O}_ Z)\) is surjective. Notice that 0-spanned is the same as saying that L is very ample. The authors prove the following: Let X be a smooth complete variety of dimension greater than or equal to 3 and L a line bundle on X. If L is 3-spanned then \(K_ X\otimes L^{n- 1}\) is 2-spanned. The case \(n=2\), which is not covered by this theorem, is studied in depth in the following preprints: 1. \textit{M. Beltrametti} et al., ``On Reider's method and higher order embeddings'' and 2. \textit{M. Beltrametti}, and \textit{A. J. Sommese}, ``On k-spannedness for projective surfaces'', both Max Planck Institut Math. preprints, No. 7 and 14 (1988).
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4079586
zbMATH Keywords: k-spanned line bundle
zbMATH Keywords: curvilinear cycles
author: E. Ballico
author: Mauro C. Beltrametti
reviewed by: N. Mohan Kumar
MaRDI profile type: Publication
cites work: Q3347989
cites work: On Reider's method and higher order embeddings
cites work: On ample divisors
cites work: Q4195061
cites work: Generalized adjunction and applications
cites work: Q3953893
cites work: On the adjunction theoretic structure of projective varieties
cites work: On the adjunction mapping
cites work: On the 2-connectedness of very ample divisors on a surface
OpenAlex ID: W1988858705
description: scientific article; zbMATH DE number 4079586