Table of Contents
Geometry
Volume 2013, Article ID 614195, 3 pages
http://dx.doi.org/10.1155/2013/614195
Research Article

Symmetric Tensor Rank and Scheme Rank: An Upper Bound in terms of Secant Varieties

Department of Mathematics, University of Trento, Povo, 38123 Trento, Italy

Received 3 June 2013; Accepted 9 August 2013

Academic Editor: Anna Fino

Copyright © 2013 E. Ballico. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be an integral and nondegenerate variety. Let be the minimal integer such that is the -secant variety of , that is, the minimal integer such that for a general there is with and , where is the linear span. Here we prove that for every there is a zero-dimensional scheme such that and ; we may take as union of points and tangent vectors of .