On the postulation of a general projection of a curve in \(P^ N\), N\(\geq 4\)
type: Item
instance of: scholarly article
title: On the postulation of a general projection of a curve in \(P^ N\), N\(\geq 4\)
zbMATH Open document ID: 0634.14036
DOI: 10.1007/BF01762421
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: Main results: (a) Fix integers N, d, g with \(N>3\), \(0\leq g\leq N-1\), \(d\geq g+N\), a smooth curve X of genus \(g\) and \(L\in Pic^ d(X)\); let \(h_ L(X)\) be the image of X by the complete linear system \(H^ 0(X,L)\); then a general projection of \(H_ L(X)\) into \({\mathbb{P}}^ N\) has maximal rank. \((b)\quad Fix\) N, g with \(N>3\), \(g\geq 0\); there is an integer d(g,N) such that for every \(d\geq d(g,N)\), for every smooth curve X of genus \(g\) and every \(L\in Pic{}^ d(X)\), the general projection of \(h_ L(X)\) into \({\mathbb{P}}^ N\) has maximal rank. The case \(N=3\) was done by the authors in Ann. Mat. Pura Appl., IV. Ser. 142, 15-48 (1985; Zbl 0591.14041)].
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14H99
zbMATH DE Number: 4031873
zbMATH Keywords: postulation
zbMATH Keywords: projective curve
zbMATH Keywords: general projection
zbMATH Keywords: maximal rank
zbMATH Keywords: Pic
author: E. Ballico
author: Ph. Ellia
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01762421
OpenAlex ID: W4242940401
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description: scientific article; zbMATH DE number 4031873