É com enorme prazer que anunciamos mais um encontro no nosso Seminário de Geometria Algébrica e Geometria Complexa da UFF. Teremos a honra de receber o prof. Hamid, da UFRJ, na quinta-feira da semana que vem:
Palestrante: Hamid Hassanzadeh (UFRJ)
Título: The Locus of Birational Maps of Polynomial Degree d on an
Arbitrary Variety X, Bir(X)_d
Resumo: A system of (n+1) homogeneous polynomials of degree d in (n+1)
variables depends on (n+1)·(n+d choose d) coefficients. A natural
question is to determine which points of this parameter space define a
birational map on P^n. In their seminal 2013 work, Jérémy Blanc and
Jean-Philippe Furter established that the set Bir(P^n)_d admits the
structure of a quasi-projective variety. In this lecture, we extend
this result to an arbitrary projective variety X. We begin by
formulating a precise notion of polynomial degree for birational maps
on an arbitrary projective variety. We then prove that, in the
corresponding parameter space, the locus of birational maps of fixed
polynomial degree carries the structure of a quasi-projective variety.
Our method is entirely commutative-algebraic. We show that the loci of
ideals in the principal class, of grade at least two, and with maximal
analytic spread, are open Zariski in the parameter space. Furthermore,
by combining effective bounds for Gröbner bases with structural
properties of the Rees algebra, we obtain bounds on the degree of the
inverse of a birational map. This talk is based on joint work with
Maral Mostafazadehfard
Data: Quinta-feira 09 de abril, 15 horas
Local: sala 407 – Bloco H – Gragoatá
Para maiores informações sobre os seminários e o histórico, consulte: