'Secant defectiveness of toric varieties' by Rick Rischter (UNIFEI)

"Secant defectiveness of toric varieties"

Talk by Rick Rischter (UNIFEI) on July 8, 2020.

The h-secant variety Sec_h(X) of a nondegenerate n-dimensional projective variety X in N-dimensional space is the Zariski closure of the union of all linear spaces spanned by collections of h points of X. The expected dimension of Sec_h(X) is the minimum between nh + h − 1 and N. The actual dimension may be smaller.

Let N be a rank-n free Abelian group and M its dual. Let P be a full
dimensional lattice polytope in the vector space over the rationals generated by M and X_P the corresponding toric variety. In this talk we discuss a new technique to give bounds on the secant defectiveness of X_P using information from the polytope P. This is a joint work just submitted
with Antonio Laface and Alex Massarenti.