We study the secant line variety of the Segre product of projective spaces
using special cumulant coordinates adapted for secant varieties. We show that
the secant variety is covered by open normal toric varieties. We prove that in
cumulant coordinates its ideal is generated by binomial quadrics. We present
new results on the local structure of the secant variety. In particular, we
show that it has rational singularities and we give a description of the
singular locus. We also classify all secant varieties that are Gorenstein.
Moreover, generalizing (Sturmfels and Zwiernik 2012), we obtain analogous
results for the tangential variety.Comment: Some improvements to previous results, with other minor changes.
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