"Toric Arrangements"

Richard Ehrenborg
University of Kentucky

Monday, September 10, 2007
4:00 pm, 113 Patterson Office Tower

Abstract:

In the 1970's Zaslavsky initiated the modern study of hyperplane arrangements. For a central hyperplane arrangement he showed that evaluating the characteristic polynomial at -1 gives the number of regions in the complement of the arrangement. For central arrangements Bayer and Sturmfels proved its flag f-vector can be determined by the intersection lattice. Billera, Ehrenborg and Readdy made this map explicit using coalgebraic techniques.

We extend the Billera-Ehrenborg-Readdy omega map to toric hyperplane arrangements. We also generalize Zaslavsky's fundamental result on the number of regions. We believe these results hint at a wealth of problems involving regular subdivisions of manifolds. I will indicate a few of these directions.

This is joint work with Margaret Readdy and Michael Slone.