Beyond positivity in Ehrhart Theory

Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou, Johanna Kristina Steinmeyer

Published 2022-10-19Version 1

We study semigroup algebras arising from lattice polytopes, compute their volume polynomials (particularizing work of Hochster), and establish strong Lefschetz properties (generalizing work of the first three authors). This resolves several conjectures concerning unimodality properties of the $h^\ast$-polynomial of lattice polytopes arising within Ehrhart theory.