%0 Journal Article %1 stapledon_ehrhart_2008 %A Stapledon, Alan %D 2008 %J 0806.4669 %K Cohomology {Hypertoric,Orbifold} %T Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties %U http://arxiv.org/abs/0806.4669 %X 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 \$\textbackslashdelta\$-polynomial of the associated Lawrence polytope. As a consequence, we deduce a formula for the Ehrhart \$\textbackslashdelta\$-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 \$\textbackslashdelta\$-polynomial.

@article{stapledon_ehrhart_2008, 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 \${\textbackslash}delta\$-polynomial of the associated Lawrence polytope. As a consequence, we deduce a formula for the Ehrhart \${\textbackslash}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 \${\textbackslash}delta\$-polynomial.}, added-at = {2009-05-11T21:36:02.000+0200}, author = {Stapledon, Alan}, biburl = {https://www.bibsonomy.org/bibtex/2fe9946a134976b485174a5b6d32d73fd/tbraden}, interhash = {5c3120b45ffba2a8273fe9483e4f8a37}, intrahash = {fe9946a134976b485174a5b6d32d73fd}, journal = {0806.4669}, keywords = {Cohomology {Hypertoric,Orbifold}}, month = {June}, timestamp = {2009-05-11T21:36:03.000+0200}, title = {Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties}, url = {http://arxiv.org/abs/0806.4669}, year = 2008 }