Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties

Details Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties

2008-06-28

arxiv.org/abs/0806.4669v1

Proc. Amer. Math. Soc. 137 (2009), 4243-4253

Mathematics

Combinatorics

10 pages

Scientific paper

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

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