INVESTIGADORES
DICKENSTEIN Alicia Marcela
congresos y reuniones científicas
Título:
Tropical duals of toric varieties
Autor/es:
A. DICKENSTEIN
Lugar:
Castro Urdiales
Reunión:
Congreso; Tropical Geometry Workshop; 2011
Institución organizadora:
Universidad de Cantabria
Resumen:
p { margin-bottom: 0.21cm; }
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.