Sandra Di Rocco: Higher order toric projective duality

Projective toric duality is the study of the behavior of the dual variety defined by a toric embedding. Via the associated lattice polytopes it explores the behavior of the discriminant of a finite set of integer points. Higher order dual varieties are natural generalizations of the classical dual varieties capturing "higher order" tangency properties of the given embedding. I will report on results on  higher order duals of projective toric embeddings.  In particular  the computation of the degree of the second dual variety of a smooth toric threefold  in geometric and  combinatorial terms will be presented. If time permits a description  of  the tropicalization of the higher  dual variety of an equivariantly embedded (not necessarily normal) toric variety will be presented. All this is joint work with A. Dickenstein and R. Piene.