Table of Contents
ISRN Geometry
Volume 2013 (2013), Article ID 704072, 4 pages
http://dx.doi.org/10.1155/2013/704072
Research Article

Rank 1 Decompositions of Symmetric Tensors Outside a Fixed Support

Department of Mathematics, University of Trento, 38123 Povo (TN), Italy

Received 18 October 2013; Accepted 12 December 2013

Academic Editors: A. M. Cegarra, R. Farnsteiner, F. B. Gallego, S. K. Kar, and P. Schenzel

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 , , denote the degree Veronese embedding of . For any , let be the minimal cardinality of such that . Identifying with a homogeneous polynomial (or a symmetric tensor), corresponds to writing as a sum of powers with a linear form (or as a sum of -powers of vectors). Here we fix an integral variety and and study a similar decomposition with and minimal. For instance, if is a linear subspace, then we prove that and classify all such that .