Algebraic and Topological Combinatorics

Special Session at the Spring Eastern Section Meeting
of the American Mathematical Society

Courant Institute, New York, NY
April 12-13, 2003



Nicholas Proudfoot
(U. C. Berkeley)


Hypertoric varieties


Abstract: A hypertoric variety is an algebraic variety that can be constructed from a real, affine arrangement of hyperplanes. Just as there is a rich interaction between toric geometry and the combinatorics of simple (or simplicial) polytopes, hypertoric geometry is deeply related to the combinatorics of arrangements.

I will define hypertoric varieties and state some results about their cohomology, with two combinatorial applications. The first is a result about the h-vector of a rationally representable matroid, due to Hausel and Sturmfels, and the second is a deformation of the Orlik-Solomon algebra of a smooth, real arrangement.

The second application is joint work with Megumi Harada (U.C. Berkeley).

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last updated: April 3, 2003