A Poisson formula for the sparse resultant
Algebraic Geometry
2015-06-12 v2 Commutative Algebra
Combinatorics
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.
Cite
@article{arxiv.1310.6617,
title = {A Poisson formula for the sparse resultant},
author = {Carlos D'Andrea and Martin Sombra},
journal= {arXiv preprint arXiv:1310.6617},
year = {2015}
}
Comments
35 pages, latex file, revised version accepted for publication in the Proceedings of the London Mathematical Society