Pré-Publication, Document De Travail Année : 2025

Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities

Résumé

We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their fundamental classes, in terms of Parseval-Rayleigh identities and differential equations, which we prove to be equivalent. We use these descriptions to establish strong Lefschetz properties. A consequence is the resolution of several conjectures concerning unimodality properties of the h * -polynomial of lattice polytopes arising within the theory of lattice polytopes.

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Dates et versions

hal-05238822 , version 1 (04-09-2025)
hal-05238822 , version 2 (15-09-2025)

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  • HAL Id : hal-05238822 , version 2

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Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou. Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities. 2025. ⟨hal-05238822v2⟩
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