Bernardi, Alessandra ; Gimigliano, Alessandro ; Idà, Monica
On the stratication of secant varieties of Veronese varieties via symmetric rank.
[Preprint]
Full text available as:
Abstract
When considering $\sigma_r(X)$, the variety of r-secant $\PP {r-1}$ to a projective variety $X$, one question which arises is what are the possible values of the $X$-rank of points on $\sigma_r(X)$, apart from the generic value $r$? This geometric problem is of particular relevance (also for Applied Math) when $X$ is a variety parameterizing some kind of tensors. We study here the case when $X$ is a Veronese variety (i.e. the case of symmetric tensors). We find the complete description of the rank strata in some cases, and we give algorithms which compute the symmetric rank.
Abstract
When considering $\sigma_r(X)$, the variety of r-secant $\PP {r-1}$ to a projective variety $X$, one question which arises is what are the possible values of the $X$-rank of points on $\sigma_r(X)$, apart from the generic value $r$? This geometric problem is of particular relevance (also for Applied Math) when $X$ is a variety parameterizing some kind of tensors. We study here the case when $X$ is a Veronese variety (i.e. the case of symmetric tensors). We find the complete description of the rank strata in some cases, and we give algorithms which compute the symmetric rank.
Document type
Preprint
Creators
Subjects
Deposit date
14 Aug 2009 10:21
Last modified
17 Feb 2016 15:04
URI
Other metadata
Document type
Preprint
Creators
Subjects
Deposit date
14 Aug 2009 10:21
Last modified
17 Feb 2016 15:04
URI
Available versions of this document
-
On the stratication of secant varieties of Veronese varieties via symmetric rank. (deposited 14 Aug 2009 10:21)
[Currently displayed]
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:
