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5 papers · 2 filters
Some Bounds for the Number of Components of Real Zero Sets of Sparse Polynomials
Daniel Perrucci
We prove that the zero set of a 4-nomial in n variables in the positive orthant has at most three connected components. This bound, which does not depend on the degree of the polyn…
Codimension Theorems for Complete Toric Varieties
David Cox, Alicia Dickenstein
Let X be a complete toric variety with homogeneous coordinate ring S. In this article, we compute upper and lower bounds for the codimension in the critical degree of ideals of S g…
Bivariate hypergeometric D-modules
Alicia Dickenstein, Laura Matusevich, Timur Sadykov
We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holo…
Multihomogeneous resultant formulae by means of complexes
A. Dickenstein, I. Emiris
We provide conditions and algorithmic tools so as to classify and construct the smallest possible determinantal formulae for multihomogeneous resultants arising from Weyman complex…
Subresultants and Generic Monomial Bases
Carlos D'Andrea, Gabriela Jeronimo
Given n polynomials in n variables of respective degrees d_1,...,d_n, and a set of monomials of cardinality d_1...d_n, we give an explicit subresultant-based polynomial expression…