Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties

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.

10 pages

References in corpus (4)

• A survey of hypertoric geometry and topology
• Ehrhart series and lattice triangulations
• Note on orbifold Chow ring of semi-projective toric Deligne-Mumford stacks
• Orbifold cohomology of hypertoric varieties