Completeness and non-speciality of linear series on space curves and deficiency of the corresponding linear series on normalization
type: Item
instance of: scholarly article
title: Completeness and non-speciality of linear series on space curves and deficiency of the corresponding linear series on normalization
zbMATH Open document ID: 0594.14009
DOI: 10.1007/BF01763173
author: N. Chiarli
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1985-01-01T00:00:00Z
review text: Let \(X\subset {\mathbb{P}}^ r\) be a reduced, irreducible curve with normalization C. Let \(A=\oplus_{n\geq 0}A_ n\) be a saturated homogeneous ideal of \(k[x_ 0,...,x_ r]\) containing strictly the homogeneous ideal of X. Let D(A) be the positive divisor of C determined by A. Fix an integer N such that for all \(n\geq N\), \(h^ 1({\mathbb{P}}^ r,{\mathcal J}_ X(n))=h^ 1(X,{\mathcal O}_ X(n))=0\). Here the author proves that for every \(n\geq N\), the natural map \(A_ n\to H^ 0(C,{\mathcal O}_ C(n)\otimes {\mathcal O}_ C(-D(A))\) is surjective. Thanks to Castelnuovo and Gruson-Lazarsfeld-Peskine, there are good bounds on N.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 3955090
zbMATH Keywords: singular curve
zbMATH Keywords: adjoint ideal
zbMATH Keywords: linear series
zbMATH Keywords: saturated homogeneous
zbMATH Keywords: ideal
zbMATH Keywords: normalization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3955090