Ranks on the Boundaries of Secant Varieties

Authors

  • Edoardo Ballico Univ. Trento

Keywords:

Secant Variety, X-Rank, Tangential Variety, Join of Two Varieties, Segre Variety, Tensor Rank

Abstract

In many cases (e.g. for many Segre or Segre-Veronese embeddings of multiprojective spaces) we prove (in characteristic 0) that a hypersurface of the b-secant variety of X\subset \mathbb{P}^r has X-rank > b. We prove it proving that the X-rank of a general point of the join of b − 2 copies of $X$ and the tangential variety of X is > b.

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Author Biography

Edoardo Ballico, Univ. Trento

Dipartimento di Matematica,

Univ. Trento,

Italy.

 

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Published

31-12-2018

How to Cite

Ballico, E. (2018). Ranks on the Boundaries of Secant Varieties. New Zealand Journal of Mathematics, 48, 31–39. Retrieved from https://nzjmath.org/index.php/NZJMATH/article/view/37

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