Residues and Resultants

Details Residues and Resultants Residues and Resultants

1997-01-31

arxiv.org/abs/alg-geom/9702001v1

Mathematics

Algebraic Geometry

Plain TeX, 22 pages

Scientific paper

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.

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