2016/03/29 by Antoine Douai, Douai, Antoine
Computer Science · Mathematics · #14C40 #14J33 #32S40 #34M35 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1603.08693
openalex publication_date 2016/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a convex polytope, we define its geometric spectrum, a stacky version of Batyrev's stringy E-functions, and we prove a stacky version of a formula of Libgober and Wood about the E-polynomial of a smooth projective variety. As an application, we get a closed formula for the variance of the geometric spectrum and a Noether's formula for two dimensional Fano polytopes (polytopes whose vertices are primitive lattice points). We also show that this geometric spectrum is equal to the algebraic spectrum of the polytope (the spectrum at infinity of a tame Laurent polynomial whose Newton polytope is the polytope alluded to). This gives an explanation and some positive answers to Hertling's conjecture about the variance of the spectrum of tame regular functions.