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

Author

Listed:
  • Edoardo Ballico

    (Department of Mathematics, University of Trento, 38123 Povo, Italy)

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 ).

Suggested Citation

  • Edoardo Ballico, 2018. "Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank," Mathematics, MDPI, vol. 6(8), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:8:p:140-:d:163776
    as

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