An asymptotic bound for secant varieties of Segre varieties
arXiv:1209.1732 · doi:10.1007/s11565-013-0175-y
Abstract
This paper studies the defectivity of secant varieties of Segre varieties. We prove that there exists an asymptotic lower estimate for the greater non-defective secant variety (without filling the ambient space) of any given Segre variety. In particular, we prove that the ratio between the greater non-defective secant variety of a Segre variety and its expected rank is lower bounded by a value depending just on the number of factors of the Segre variety. Moreover, in the final section, we present some results obtained by explicit computation, proving the non-defectivity of all the secant varieties of Segre varieties of the shape (P^n)^4, with 1 < n < 11, except at most σ_199((P^8)^4) and σ_357((P^10)^4).
arXiv comment14 pages