Beyond positivity in Ehrhart Theory

Beyond positivity in Ehrhart Theory

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^\as...

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Hauptverfasser: Adiprasito, Karim Alexander, Papadakis, Stavros Argyrios, Petrotou, Vasiliki, Steinmeyer, Johanna Kristina
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Geometry
Mathematics - Combinatorics
Mathematics - Commutative Algebra
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Beschreibung
Zusammenfassung: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.
DOI:10.48550/arxiv.2210.10734