2013/10/31 by Carlos D'Andrea, Carlos D’Andrea, Martín Sombra +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Connection (principal bundle) #Intersection (aeronautics) #Intersection theory #Poisson distribution #Poisson summation formula #Polynomial and algebraic computation #Product (mathematics) #math.AC #math.AG #math.CO #msc:13P15 #msc:14M25 #msc:52B20
paper · pdf · doi:10.1112/plms/pdu069
35 pages, latex file, revised version accepted for publication in the Proceedings of the London Mathematical Society
arxiv created 2014/12/17 · openalex publication_date 2015/02/06 · arxiv updated 2015/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 Rémond. This connection allows to study sparse resultants using multiprojective elimination theory and intersection theory of toric varieties.