Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908544389873664 |
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| author | Adiprasito, Karim Alexander Papadakis, Stavros Argyrios Petrotou, Vasiliki |
| author_facet | Adiprasito, Karim Alexander Papadakis, Stavros Argyrios Petrotou, Vasiliki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities Adiprasito, Karim Alexander Papadakis, Stavros Argyrios Petrotou, Vasiliki Combinatorics Commutative Algebra Algebraic Geometry 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. |
| title | Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities |
| topic | Combinatorics Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2509.14152 |