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Pré-Publication, Document De Travail Année : 2016

Global spectra, polytopes and stacky invariants

Résumé

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).
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Dates et versions

hal-01294940 , version 1 (30-03-2016)

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Antoine Douai. Global spectra, polytopes and stacky invariants. 2016. ⟨hal-01294940⟩
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