Ranks on the Boundaries of Secant Varieties
Keywords:Secant Variety, X-Rank, Tangential Variety, Join of Two Varieties, Segre Variety, Tensor Rank
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 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.