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Proceedings of the American Mathematical Society
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Ehrhart theory for Lawrence polytopes and orbifold cohomology of hypertoric varieties

Author(s): Alan Stapledon
Journal: Proc. Amer. Math. Soc. 137 (2009), 4243-4253.
MSC (2000): Primary 52B20, 53C26, 52C35
Posted: July 23, 2009
MathSciNet review: 2538585
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Abstract | References | Similar articles | Additional information

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: 10.1090/S0002-9939-09-09969-9
PII: S 0002-9939(09)09969-9
Received by editor(s): July 2, 2008,
Received by editor(s) in revised form: March 12, 2009
Posted: July 23, 2009
Additional Notes: The author would like to thank Nicholas Proudfoot for some useful comments.
Communicated by: Jim Haglund
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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