INVESTIGADORES
DICKENSTEIN Alicia Marcela
congresos y reuniones científicas
Título:
Tropical duals of toric varieties
Autor/es:
A, DICKENSTEIN
Lugar:
Warwick
Reunión:
Congreso; Tropical day; 2012
Institución organizadora:
University of Warwick
Resumen:
Let X be a projective toric variety
rationally parametrized by monomials with exponents in a lattice
configuration A of cardinality n. For any given positive integer k, the k-th
dual variety X^(k) is defined as the closure in the dual projective space of
all hyperplanes that intersect X at a smooth point and contain the k-th
osculating space at this point, generalizing the classical definition of the projective
dual for k=1.
In this talk, I will present the following results. In joint work with L.
Tabera, we define tropical Euler derivatives to characterize those weights p in
R^n such that the tropical polynomial f with support A and coefficients p,
defines a singular tropical hypersurface. With this approach, we recover the
description obtained in collaboration with E.M. Feichtner and B. Sturmfels of the tropicalization of
the A-discriminant variety, and we locate the singular points. With
similar methods, in joint work with S. di Rocco and R. Piene we describe those
weights p for which f lies in the tropicalization of X^(k) for any k.