Residues and Resultants

Cattani, Eduardo; Dickenstein, Alicia; Sturmfels, Bernd

Residues and Resultants

Authors

Cattani, Eduardo

Dickenstein, Alicia

Sturmfels, Bernd

Description

Resultants, Jacobians and residues are basic invariants of multivariate polynomial systems. We examine their interrelations in the context of toric geometry. The global residue in the torus, studied by Khovanskii, is the sum over local Grothendieck residues at the zeros of $n$ Laurent polynomials in $n$ variables. Cox introduced the related notion of the toric residue relative to $n+1$ divisors on an $n$-dimensional toric variety. We establish denominator formulas in terms of sparse resultants for both the toric residue and the global residue in the torus. A byproduct is a determinantal formula for resultants based on Jacobians.
Plain TeX, 22 pages