Intersection cohomology of hypertoric varieties

Proudfoot, Nicholas; Webster, Benjamin

doi:10.1090/S1056-3911-06-00448-6

Authors: Nicholas Proudfoot and Benjamin Webster
Journal: J. Algebraic Geom. 16 (2007), 39-63
DOI: https://doi.org/10.1090/S1056-3911-06-00448-6
Published electronically: August 22, 2006
MathSciNet review: 2257319
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Abstract | References | Additional Information

Abstract: A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics of hyperplane arrangements and matroids. Using finite field methods, we obtain combinatorial descriptions of the Betti numbers of hypertoric varieties, both for ordinary cohomology in the smooth case and intersection cohomology in the singular case. We also introduce a conjectural ring structure on the intersection cohomology of a hypertoric variety.

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Additional Information

Nicholas Proudfoot
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Address at time of publication: Department of Mathematics, Columbia University, 2990 Broadway, MC 4406, New York, New York 10027
MR Author ID: 689525
Email: njp@math.utexas.edu

Benjamin Webster
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
MR Author ID: 794563
Email: bwebste@math.berkeley.edu

Received by editor(s): May 4, 2005
Received by editor(s) in revised form: January 16, 2006
Published electronically: August 22, 2006
Additional Notes: The first author was supported by the Clay Liftoff Fellowship and the National Science Foundation Postdoctoral Research Fellowship. The second author was supported by the National Science Foundation Graduate Research Fellowship.