Session A2 - Computational Algebraic Geometry
July 11, 14:30 ~ 14:55 - Room B5
Factorization of sparse bivariate polynomials
ICREA & Universitat de Barcelona, Spain - email@example.com
It is expected that, for a given sparse univariate polynomial over the rationals, its non-cyclotomic irreducible factors are also sparse. This is a vague principle that takes a more precise form in an old (and still open) conjecture of Schinzel, on the irreducible factors in families of polynomials with fixed coefficients and varying monomials.
In this talk, I will present a theorem giving an analogue of Schinzel conjecture for polynomials over a function field. This result gives a description of the irreducible factors in families of bivariate polynomials over a field of characteristic zero.
Its proof is based on a toric version of Bertini's theorem.
Joint work with Francesco Amoroso (Université de Caen, France).