Higher syzygies of hyperelliptic curves
type: Item
instance of: scholarly article
title: Higher syzygies of hyperelliptic curves
zbMATH Open document ID: 1189.14041
author: Euisung Park
published in: Journal of Pure and Applied Algebra
publication date: 2009-11-23T00:00:00Z
review text: Let \(K\) be an algebraically closed field of arbitrary characteristic and let \(\mathbb{P}^r\) be the projective \(r\)-space over \(K.\) In the theory of projective curves, one of the most important problems is to understand how a curve can map to projective spaces. Let \(L\) be a very ample line bundles of degree \(d\leq 2g\) on a hyperelliptic curve \(X\). Let \(\phi:X\to \mathbb{P}^r\) be the map induced by \(L.\) In this paper a couple of integers, the factorization type of \(L,\) is associated to \(L\) and it is shown that the Hartshorne-Rao module and the graded Betti numbers of the curve embedded by \(|L|\) are precisely determined by the factorization type.
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 5637049
zbMATH Keywords: Hyperelliptic curves
zbMATH Keywords: embedding
zbMATH Keywords: Hartshorne-Rao module
zbMATH Keywords: syzygies
reviewed by: Giuseppe Zappalà
MaRDI profile type: Publication
full work available at URL: j.jpaa.2009.04.006
OpenAlex ID: W2030047478
cites work: Q4123438
cites work: Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
cites work: Q3824513
cites work: On graded Betti numbers and geometrical properties of projective varieties
cites work: On the projective normality of complete linear series on an algebraic curve
cites work: Some generalizations of Castelnuovo's lemma on zero-dimensional schemes
cites work: Linear free resolutions and minimal multiplicity
cites work: The Geometry of Syzygies
cites work: Restricting linear syzygies: algebra and geometry
cites work: Determinantal Equations for Curves of High Degree
cites work: The canonical model of a singular curve
cites work: Lectures on Curves on an Algebraic Surface. (AM-59)
cites work: Hyperelliptic Gorenstein curves
cites work: Q3592298
cites work: Arithmetically Buchsbaum divisors on varieties of minimal degree
DOI: 10.1016/J.JPAA.2009.04.006
description: scientific article; zbMATH DE number 5637049