Postulation and gonality for projective curves
type: Item
instance of: scholarly article
title: Postulation and gonality for projective curves
zbMATH Open document ID: 0692.14017
author: E. Ballico
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108113
review text: A curve Z in \({\mathbb{P}}^ n\) enjoys the maximal rank property if the natural restriction map \(H^ 0({\mathbb{P}}^ n,{\mathcal O}_{{\mathbb{P}}^ n}(k))\to H^ 0(Z,{\mathcal O}_ Z(k))\) has maximal rank for every positive integer k. A smooth projective curve \(Y\subseteq {\mathbb{P}}^ n\) is said to be canonical if the hyperplane sections of Y are canonical. The author relates these properties to intrinsic properties of the curve, proving that for \(g>n\), \(n>3\) the general trigonal (bielliptic) canonical curve of genus g in \({\mathbb{P}}^ n\) has maximal rank. He also proves that for all \(n,d,g\in {\mathbb{N}},\) \(g>n>3,\) \(d>2g,\) a general embedding of degree d in \({\mathbb{P}}^ n\) of a general hyperelliptic curve of genus g has maximal rank. Both results are proven by degeneration arguments.
reviewed by: Rita Pardini
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 4132332
zbMATH Keywords: postulation
zbMATH Keywords: gonality
zbMATH Keywords: maximal rank property
zbMATH Keywords: canonical curve
zbMATH Keywords: embedding
zbMATH Keywords: degeneration
MaRDI profile type: Publication
cites work: Generic curves of small genus in \(P^3\) are of maximal rank
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cites work: A remark on the syzygies of the generic canonical curves
cites work: On the Kodaira dimension of the moduli space of curves
cites work: Sur la postulation generique des courbes rationnelles
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description: scientific article; zbMATH DE number 4132332