Stratification of the fourth secant variety of Veronese variety via the symmetric rank.

Ballico, Edoardo ; Bernardi, Alessandra (2010) Stratification of the fourth secant variety of Veronese variety via the symmetric rank. [Preprint]
Full text available as:
[img]
Preview
PDF
Download (282kB) | Preview

Abstract

If $X\subset \PP n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \PP n$ is defined to be the minimum integer $r$ such that $P$ belongs to the span of $r$ points of $X$. We describe the complete stratification of the fourth secant variety of any Veronese variety $X$ via the $X$-rank. This result has an equivalent translation in terms both of symmetric tensors and homogeneous polynomials. It allows to classify all the possible integers $r$ that can occur in the minimal decomposition of either a symmetric tensor or a homogeneous polynomials of $X$-border rank $4$ (see Not. \ref{border}) as a linear combination of either completely decomposable tensors or powers of linear forms respectively.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Ballico, Edoardo
Bernardi, Alessandra
Keywords
Rank of tensors, Polynomial decomposition, Secant varieties, Veronese Varieties
Subjects
DOI
Deposit date
21 May 2010 08:03
Last modified
16 May 2011 12:13
URI

Other metadata

This work may be freely consulted and used, may be reproduced on a permanent basis in a digital format (i.e. saving) and can be printed on paper with own personal equipment (without availing of third -parties services), for strictly and exclusively personal, research or teaching purposes, with express exclusion of any direct or indirect commercial use, unless otherwise expressly agreed between the user and the author or the right holder. It is also allowed, for the same purposes mentioned above, the retransmission via telecommunication network, the distribution or sending in any form of the work, including the personal redirection (e-mail), provided it is always clearly indicated the complete link to the page of the Alma DL Site in which the work is displayed. All other rights are reserved.

Downloads

Downloads

Staff only: View the document

^