Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank

Edoardo Ballico
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Edoardo Ballico: Department of Mathematics, University of Trento, 38123 Povo, Italy

Mathematics, 2018, vol. 6, issue 8, 1-9

Abstract: Let X ⊂ P r be an integral and non-degenerate variety. We study when a finite set S ⊂ X evinces the X -rank of the general point of the linear span of S . We give a criterion when X is the order d Veronese embedding X n , d of P n and | S | ≤ ( n + ⌊ d / 2 ⌋ n ) . For the tensor rank, we describe the cases with | S | ≤ 3 . For X n , d , we raise some questions of the maximum rank for d ? 0 (for a fixed n ) and for n ? 0 (for a fixed d ).

Keywords: X-rank; symmetric tensor rank; tensor rank; veronese variety; segre variety (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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