On \(d\)-spannedness of the adjoint bundles on polarized manifolds
type: Item
instance of: scholarly article
title: On \(d\)-spannedness of the adjoint bundles on polarized manifolds
zbMATH Open document ID: 0926.14020
author: Takeshi Kawachi
published in: Kodai Mathematical Journal
publication date: 1999-11-16T00:00:00Z
review text: Fix \(L\in\text{Pic}(X)\) a with \(X\) a smooth \(n\)-dimensional projective variety. \(L\) is said \(d\)-spanned \((d\geq 0)\) if for every curvilinear 0-dimensional subscheme \(Z\) of \(X\) with \(\text{length} (Z)\leq d+1\) the restriction map \(H^0(X,L)\to H^0(Z,L| Z)\) is surjective. Here the author gives for all integers \(n,d\) a nice example of a pair \((X,L)\) as above with \(L\) ample and \(d\)-spanned but for which \(K_X+ (n+d)L\) is not \(d\)-spanned.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14C22
zbMATH DE Number: 1269767
zbMATH Keywords: Picard group
zbMATH Keywords: \(d\)-spanned line bundle
zbMATH Keywords: smooth polarized variety
zbMATH Keywords: Fujita conjecture
zbMATH Keywords: ample line bundle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043872
OpenAlex ID: W1971255099
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DOI: 10.2996/KMJ/1138043872
description: scientific article; zbMATH DE number 1269767