8 research outputs found
An asymptotic bound for secant varieties of Segre varieties
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
\sigma_199((P^8)^4) and \sigma_357((P^10)^4).Comment: 14 page
Real rank boundaries and loci of forms
In this article we study forbidden loci and typical ranks of forms with
respect to the embeddings of given by the line
bundles . We introduce the Ranestad-Schreyer locus corresponding to
supports of non-reduced apolar schemes. We show that, in those cases, this is
contained in the forbidden locus. Furthermore, for these embeddings, we give a
component of the real rank boundary, the hypersurface dividing the minimal
typical rank from higher ones. These results generalize to a class of
embeddings of . Finally, in connection with real
rank boundaries, we give a new interpretation of the
hyperdeterminant.Comment: 17 p