Degree bounds for the sparse Nullstellensatz

JERONIMO, GABRIELA

Berna

Conferencia; SIAM Conference on Applied Algebraic Geometry; 2019

Society for Industrial and Applied Mathematics

We will present new upper bounds both the degrees in Hilbert´s Nullstellensatz and for the Noether exponent of a polynomial ideal in terms of mixed volumes of convex sets associated with the supports of a finite family of given generators. Our main results are the first upper bounds valid for arbitrary polynomial systems that distinguish the different supports of the polynomials. In the mixed sparse setting, they can be considerably smaller than previously known bounds. This is joint work with María Isabel Herrero and Juan Sabia (Universidad de Buenos Aires and CONICET, Argentina).