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Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties


Author: Alan Stapledon
Journal: Proc. Amer. Math. Soc. 137 (2009), 4243-4253
MSC (2000): Primary 52B20, 53C26, 52C35
DOI: https://doi.org/10.1090/S0002-9939-09-09969-9
Published electronically: July 23, 2009
MathSciNet review: 2538585
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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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Additional Information

Alan Stapledon
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: astapldn@umich.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09969-9
Received by editor(s): July 2, 2008
Received by editor(s) in revised form: March 12, 2009
Published electronically: July 23, 2009
Additional Notes: The author would like to thank Nicholas Proudfoot for some useful comments.
Communicated by: Jim Haglund
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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