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arXiv · 0806.4669

Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties

Alan Stapledon
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Abstract

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 $δ$-polynomial of the associated Lawrence polytope. As a consequence, we deduce a formula for the Ehrhart $δ$-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 $δ$-polynomial.

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Alan Stapledon. 2008-06-28. Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties. https://arxiv.org/abs/0806.4669

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