INVESTIGADORES
DICKENSTEIN Alicia Marcela
congresos y reuniones científicas
Título:
Mixed discriminants
Autor/es:
A, DICKENSTEIN
Lugar:
Rio de Janeiro
Reunión:
Seminario; Seminario de Geometría Algebraica; 2012
Institución organizadora:
IMPA
Resumen:
The mixed discriminant of n Laurent
polynomials in n variables with fixed support is the irreducible polynomial in
the coefficients which vanishes whenever two of the roots coincide. It
represents the variety of ill-posed systems. By means of the Cayley trick, we
can express the mixed discriminant as an A-discriminant in the sense of
Gelfand, Kapranov and Zelevinski. Our goal is to characterize its degree. I
will discuss in detail the case of two plane curves where an explicit degree
formula can be provided. In the case of two dense polynomials, this formula
recovers the classical tact invariant of Salmon. Finally, inspired by the
tropical approach to computing A-discriminants, I will show that the degree of
the mixed discriminant is a piecewise linear function in the Plücker coordinates
of a mixed Grassmannian. Joint work with E. Cattani, M. A. Cueto, S. Di Rocco
and B. Sturmfels.
