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

By Edoardo Ballico, Alessandra Bernardi. 2010

60 citations recorded by the source corpus.

Abstract. If is a projective non-degenerate variety, the X-rank of a point 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 either of symmetric tensors or of homogeneous polynomials. It allows to classify all the possible integers r that can occur in the minimal decomposition of a homogeneous polynomial of X-border rank (i.e. contained in the fourth secant variety) as a linear combination of powers of linear forms.

Subfields: Computational Mathematics

View Paper: https://www.semanticscholar.org/paper/687f5c9608befb63edee193cc199be95ca7b6966