On postulation of curves: Embeddings by complete linear series
type: Item
instance of: scholarly article
title: On postulation of curves: Embeddings by complete linear series
zbMATH Open document ID: 0536.14010
DOI: 10.1007/BF01247570
author: E. Ballico
author: Ph. Ellia
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: A closed subscheme C in \({\mathbb{P}}^ n\) is said to be of maximal rank if for every \(k\geq 0\) the restriction map \(r_ C(k):H^ 0({\mathbb{P}}^ n,{\mathcal O}_{{\mathbb{P}}^ n}(k))\to H^ 0(C,{\mathcal O}_ C(k))\) has maximal rank. Here we prove the following theorem. Let d,g be positive integers satisfying \(d\geq g+1+\sqrt{g};\) let X be a general smooth, complete curve of genus g; then the general embedding of X into \({\mathbb{P}}^{d-g}\) by a non-special complete linear system has maximal rank. First we prove the theorem for a suitable reducible curve Y in \({\mathbb{P}}^{d-g}\) and then we apply deformation theory [\textit{E. Sernesi}, ''On the existence of certain families of curves'', Invent. Math. 75, 25-57 (1984)] to show that Y can be smoothed.
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14D15
zbMATH DE Number: 3851255
zbMATH Keywords: embeddings by complete linear series
zbMATH Keywords: maximal rank subscheme
zbMATH Keywords: smooth complete curve
zbMATH Keywords: deformation theory
MaRDI profile type: Publication
cites work: Divisors on general curves and cuspidal rational curves
cites work: Stable curves and special divisors: Petri's conjecture
cites work: Q4195061
cites work: Q4143433
cites work: Sur la postulation generique des courbes rationnelles
cites work: On the equations defining a projective curve embedded by a non-special divisor
cites work: A note of Shimura's paper: Discontinuous groups and Abelian varieties
cites work: On Petri's analysis of the linear system of quadrics through a canonical curve
cites work: On the existence of certain families of curves
full work available at URL: https://doi.org/10.1007/bf01247570
OpenAlex ID: W2084493101
description: scientific article; zbMATH DE number 3851255