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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…
Elimination Theory in Codimension Two
Alicia Dickenstein, Bernd Sturmfels
New formulas are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. Exact descriptions are also given for th…
Explicit formulas for the multivariate resultant
Carlos D'Andrea, Alicia Dickenstein
We present formulas for the homogenous multivariate resultant as a quotient of two determinants. They extend classical Macaulay formulas, and involve matrices of considerably small…
Rational Hypergeometric Functions
Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that…