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Preprints, Working Papers, ... Year : 2011

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

Abstract

If $X\subset \mathbb{P}^n$ is a projective non degenerate variety, the $X$-rank of a point $P\in \mathbb{P}^n$ 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 polynomial of $X$-border rank $4$ (i.e. contained in the fourth secant variety) as a linear combination of either completely decomposable tensors or powers of linear forms respectively.
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Dates and versions

inria-00612460 , version 1 (29-07-2011)
inria-00612460 , version 2 (28-11-2011)

Identifiers

  • HAL Id : inria-00612460 , version 2

Cite

Edoardo Ballico, Alessandra Bernardi. Stratification of the fourth secant variety of Veronese variety via the symmetric rank. 2011. ⟨inria-00612460v2⟩
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