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An asymptotic bound for secant varieties of Segre varieties (1209.1732v1)
Published 8 Sep 2012 in math.AG
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 (Pn)4, with 1 < n < 11, except at most \sigma_199((P8)4) and \sigma_357((P10)4).