![](https://d3ilqtpdwi981i.cloudfront.net/zn-cwhaftP6tnWLYq4GwnsJZssI=/425x550/smart/https://bepress-attached-resources.s3.amazonaws.com/uploads/42/c1/89/42c18948-71d2-4109-a4bd-16d3160d8a3c/thumbnail_741bd3f3-00f7-4257-be8a-016bca2036bd.jpg)
Article
Residues and Resultants
Journal of Mathematical Sciences
Publication Date
1997
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.
Pages
119-148
Citation Information
E Cattani, Alicia Dickenstein and Bernd Sturmfels. "Residues and Resultants" Journal of Mathematical Sciences Vol. 5 Iss. 1 (1997) Available at: http://works.bepress.com/eduardo_cattani/13/
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