On postulation of curves in \({\mathbb{P}}^4\)
type: Item
instance of: scholarly article
title: On postulation of curves in \({\mathbb{P}}^4\)
zbMATH Open document ID: 0535.14015
DOI: 10.1007/BF01304209
author: E. Ballico
author: Ph. Ellia
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173532
review text: We say that a curve \(C\subset {\mathbb{P}}^ n\) has maximal rank if for every \(k\geq 0\) the restriction map \(H^ 0({\mathbb{P}}^ n,{\mathcal O}_{{\mathbb{P}}^ n}(k))\to H^ 0(C,{\mathcal O}_ C(k))\) is either injective or surjective. The maximal rank conjecture states that a general embedding of a general smooth curve of genus g has maximal rank. In this paper we prove this conjecture for non special embeddings in \({\mathbb{P}}^ 4\). The proof uses the method of \textit{R. Hartshorne} and \textit{A. Hirschowitz} [``Droites en position generale dans \({\mathbb{P}}^ n\)'' in Algebraic Geometry, Proc. int. Conf., La Rábida/Spain 1981, Lect. Notes Math. 961, 169-188 (1982; Zbl 0555.14011)] and \textit{A. Hirschowitz} [Acta Math. 146, 209-230 (1981; Zbl 0475.14027)] to show inductively the existence of a reducible curve with maximal rank.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 3849400
zbMATH Keywords: hyperplane section
zbMATH Keywords: genus
zbMATH Keywords: moduli
zbMATH Keywords: semicontinuity
zbMATH Keywords: non special embeddings in projective 4-space
zbMATH Keywords: maximal rank conjecture
zbMATH Keywords: embedding of a general smooth curve
MaRDI profile type: Publication
cites work: Q3693625
cites work: Sur la postulation generique des courbes rationnelles
cites work: On the existence of certain families of curves
OpenAlex ID: W2071514098
description: scientific article; zbMATH DE number 3849400