Publication Date

1997

Journal or Book Title

Journal of Mathematical Sciences

Abstract

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.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://repository.dl.itc.u-tokyo.ac.jp/dspace/handle/2261/1350

http://journal.ms.u-tokyo.ac.jp/pdf/jms050106.pdf

Pages

119-148

Volume

5

Issue

1

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