Arithmetic and topology of hypertoric varieties

Details Arithmetic and topology of hypertoric varieties Arithmetic and topology of hypertoric varieties

2004-11-16

arxiv.org/abs/math/0411350v4

Journal of Algebraic Geometry 16 (2007), 39-63.

Mathematics

Algebraic Geometry

22 pages, 1 figure. Final version, to be published in the Journal of Algebraic Geometry

Scientific paper

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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