A Poisson formula for the sparse resultant

Abstract

We present a Poisson formula for sparse resultants and a formula for the product of the roots of a family of Laurent polynomials, which are valid for arbitrary families of supports. To obtain these formulae, we show that the sparse resultant associated to a family of supports can be identified with the resultant of a suitable multiprojective toric cycle in the sense of Remond. This connection allows to study sparse resultants using multiprojective elimination theory and intersection theory of toric varieties.

35 pages, latex file, revised version accepted for publication in the Proceedings of the London Mathematical Society

Cited by in corpus (4)

• Hyperdeterminants from the $E_8$ Discriminant
• Solving sparse polynomial systems using Groebner bases and resultants
• Zero Distribution of Random Bernoulli Polynomial Mappings
• A package for computations with sparse resultants