On the postulation of canonical curves in \(\mathbb P^3\)
type: Item
instance of: scholarly article
title: On the postulation of canonical curves in \(\mathbb P^3\)
zbMATH Open document ID: 0546.14018
DOI: 10.1007/BF02384377
author: E. Ballico
published in: Arkiv för Matematik
publication date: 1984-01-01T00:00:00Z
review text: Here we prove the existence of smooth curves \(C\subset\mathbb P^3\) of genus \(g\) with \(\mathcal O_C(1)\cong\omega_C\) and maximal rank if \(g=7,8,9\) or \(11\). For the proof we use two results about degeneration of curves; one of them is to be found in the author's joint paper with \textit{P. Ellia} in [Algebraic Geometry - Open Problems, Proc. Conf. Ravello/It. 1982, Lect. Notes Math. 997, 1--15 (1983; Zbl 0512.14017); the second one was proved independently by \textit{E. Sernesi} [Invent. Math. 75, 25--57 (1984; Zbl 0541.14024)], and by \textit{R. Hartshorne} and \textit{A. Hirschowitz} (preprint).
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14B10
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 3869507
zbMATH Keywords: canonical divisor
zbMATH Keywords: degeneration
zbMATH Keywords: degree
zbMATH Keywords: deformation
zbMATH Keywords: existence of smooth curves of genus g
MaRDI profile type: Publication
cites work: Q4750779
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full work available at URL: https://doi.org/10.1007/bf02384377
OpenAlex ID: W1984737043
description: scientific article; zbMATH DE number 3869507