Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties
We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are equal to the coefficients of the Ehrhart δ\delta-polynomial of...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2009-12, Vol.137 (12), p.4243-4253 |
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| container_title | Proceedings of the American Mathematical Society |
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| creator | Stapledon, Alan |
| description | We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are equal to the coefficients of the Ehrhart δ\delta-polynomial of the associated Lawrence polytope. As a consequence, we deduce a formula for the Ehrhart δ\delta-polynomial of a Lawrence polytope and use the injective part of the Hard Lefschetz Theorem for hypertoric varieties to deduce some inequalities between the coefficients of the δ\delta-polynomial. |
| doi_str_mv | 10.1090/S0002-9939-09-09969-9 |
| format | Article |
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| source | Jstor Complete Legacy; American Mathematical Society Publications; American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics |
| subjects | Convex and discrete geometry Discrete mathematics Exact sciences and technology General mathematics General, history and biography Geometry Hyperplanes Integers Mathematical lattices Mathematical theorems Mathematics Matroids Polynomials Polytopes Research article Sciences and techniques of general use Vertices |
| title | Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties |
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