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Global spectra, polytopes and stacky invariants

By Antoine Douai

Abstract

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, as a consequence, for the variance of the spectrum at infinity of tame Laurent polynomials. This gives an explanation and positive answers to Hertling's conjecture about the variance of the spectrum of tame regular functions, but also a Noether's formula for two dimensional Fano polytopes (polytopes whose vertices are primitive lattice points)

Topics: [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]
Publisher: HAL CCSD
Year: 2016
OAI identifier: oai:HAL:hal-01294940v1
Provided by: HAL-UNICE
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