Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties

Stapledon, Alan

doi:10.1090/S0002-9939-09-09969-9

Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties
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by Alan Stapledon

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

DOI: https://doi.org/10.1090/S0002-9939-09-09969-9

Published electronically: July 23, 2009

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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 $\delta$-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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