1 citations · 1 across the 7 of their papers we have counts for
8 papers
Sparse systems and algorithmic equidimensional decomposition
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with pre…
Curve valuations and mixed volumes in the implicitization of rational varieties
Alicia Dickenstein, Maria Isabel Herrero, Bernard Mourrain
We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend resu…
On degree bounds for the sparse Nullstellensatz
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We prove new upper bounds for the degrees in Hilbert's Nullstellensatz and for the Noether exponent of polynomial ideals in terms of the monomial structure of the polynomials invol…
On the multiplicity of isolated roots of sparse polynomial systems
María Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We give formulas for the multiplicity of any affine isolated zero of a generic polynomial system of n equations in n unknowns with prescribed sets of monomials. First, we consider…
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials
Alicia Dickenstein, Maria Isabel Herrero, Luis Felipe Tabera
We give a description of the tropical variety of univariate polynomials of degree n having two double roots. As a set, it is given as the union of three types of maximal cones of d…
Puiseux expansions and non-isolated points in algebraic varieties
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux se…
Elimination for generic sparse polynomial systems
María Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We present a new probabilistic symbolic algorithm that, given a variety defined in an n-dimensional affine space by a generic sparse system with fixed supports, computes the Zarisk…
Affine solution sets of sparse polynomial systems
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial con…