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

2025/09/17 by Karim Adiprasito, Adiprasito, Karim Alexander, Stavros Argyrios Papadakis +3 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2509.14152

openalex publication_date 2025/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Parseval-Rayleigh identities for homogeneous complete intersections

Related

• Beyond positivity in Ehrhart Theory
• Lattice polytopes with a given h^*-polynomial
• Polyhedra, lattice structures, and extensions of semigroups
• An Upper Bound Theorem concerning lattice polytopes
• The mixed degree of families of lattice polytopes