Symmetric Tensor Rank and Scheme Rank: An Upper Bound in terms of Secant Varieties. (8th September 2013)

• Record Type: Journal Article
• Authors: Ballico, E.
• Other Names: Fino Anna Academic Editor.
• Is Part Of: Geometry. Volume 2013(2013)
• Publication Date: 2013-09-08
• Subjects: Geometry -- Periodicals; Geometry; Periodicals; 516
• DOI: 10.1155/2013/614195
• Languages: English
• ISSNs: 2314-422X

Abstract

Abstract : Let X ⊂ ℙ r be an integral and nondegenerate variety. Let c be the minimal integer such that ℙ r is the c -secant variety of X, that is, the minimal integer c such that for a general O ∈ ℙ r there is S ⊂ X with # ( S ) = c and O ∈ 〈 S 〉, where 〈 〉 is the linear span. Here we prove that for every P ∈ ℙ r there is a zero-dimensional scheme Z ⊂ X such that P ∈ 〈 Z 〉 and deg ( Z ) ≤ 2 c ; we may take Z as union of points and tangent vectors of X reg .