Syzygies of the secant variety of a curve

Sidman, Jessica; Vermeire, Peter

doi:10.2140/ant.2009.3.445

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Syzygies of the secant variety of a curve

Jessica Sidman and Peter Vermeire

Vol. 3 (2009), No. 4, 445–465

DOI: 10.2140/ant.2009.3.445

Abstract

We show the secant variety of a linearly normal smooth curve of degree at least $2 g + 3$ is arithmetically Cohen–Macaulay, and we use this information to study the graded Betti numbers of the secant variety.

Keywords

syzygies, secant varieties, projective curves, graded Betti numbers

Mathematical Subject Classification 2000

Primary: 13D02

Secondary: 14N05, 14H99, 14F05

Milestones

Received: 1 September 2008

Revised: 1 April 2009

Accepted: 29 April 2009

Published: 15 June 2009

Authors

Jessica Sidman
Mount Holyoke College Department of Mathematics and Statistics 415A Clapp Lab South Hadley, MA 01075 United States

Peter Vermeire
Central Michigan University Department of Mathematics 214 Pearce Mount Pleasant, MI 48859 United States

Vol. 3, No. 4, 2009