Ehrhart polynomials and stringy Betti numbers

DOI10.1007/s00208-005-0691-xzbMath1082.52007arXivmath/0504486OpenAlexW2058519988MaRDI QIDQ2575648

Sam Payne, Mircea Mustaţă

Publication date: 6 December 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504486

zbMATH Keywords

Gorenstein toric varietyBetti numberEhrhart polynomialrational generating functionlattice polytopereflexive polytopelattice point enumeration

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25)

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Inequalities and Ehrhart $\delta $-vectors, \(h\)-vectors of Gorenstein polytopes, Detecting the integer decomposition property and Ehrhart unimodality in reflexive simplices, Unimodality questions for integrally closed lattice polytopes, Gorenstein polytopes and their stringy \(E\)-functions, Nearly Gorenstein polytopes, Unimodality of \(\delta \)-vectors of lattice polytopes and two related properties, Stringy Hodge numbers of strictly canonical nondegenerate singularities, Weighted Ehrhart theory and orbifold cohomology, Ehrhart series, unimodality, and integrally closed reflexive polytopes, Hard Lefschetz properties and distribution of spectra in singularity theory and Ehrhart theory, Global spectra, polytopes and stacky invariants, Ehrhart series and lattice triangulations, On smooth Gorenstein polytopes, On the hard Lefschetz property of stringy Hodge numbers, Existence of unimodular triangulations — positive results, Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials, The 𝐬-Eulerian polynomials have only real roots, Flow polytopes and the graph of reflexive polytopes

Cites Work

• A new cohomology theory of orbifold
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• Special simplices and Gorenstein toric rings.
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Introduction to Toric Varieties. (AM-131)
• The orbifold Chow ring of toric Deligne-Mumford stacks
• Star-Shaped Complexes and Ehrhart Polynomials
• Twisted jets, motivic measures and orbifold cohomology
• Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley
• Hodge structures for orbifold cohomology
• Combinatorics and commutative algebra
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