Equations defining secant varieties: geometry and computation
Abstract
In the 1980's, work of Green and Lazarsfeld helped to uncover the beautiful interplay between the geometry of the embedding of a curve and the syzygies of its defining equations. Similar results hold for the first secant variety of a curve, and there is a natural conjectural picture extending to higher secant varieties as well. We present an introduction to the algebra and geometry used in previous work of the authors to study syzygies of secant varieties of curves with an emphasis on examples of explicit computations and elementary cases that illustrate the geometric principles at work.
Keywords
Cite
@article{arxiv.0910.0989,
title = {Equations defining secant varieties: geometry and computation},
author = {Jessica Sidman and Peter Vermeire},
journal= {arXiv preprint arXiv:0910.0989},
year = {2012}
}
Comments
v1: 2 figures; written for the proceedings of the Abel Symposium 2009; v2: minor changes in exposition, Macaulay 2 code added; v3: hypothesis of normality added in Theorems 5 and 8. See Remarks 4 and 9 for explanation of the additional hypotheses; v4: typos fixed