Ranks on the Boundaries of Secant Varieties

Edoardo Ballico

doi:10.53733/37

Ranks on the Boundaries of Secant Varieties

Authors

Edoardo Ballico Univ. Trento

DOI:

https://doi.org/10.53733/37

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.