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MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation
Geometric Mathematical Physics Seminar
Tuesday, 27 July 2004, at 14:15 in Aud. D3
Annette A'Campo-Neuen
Basel
Projective Toric Varieties and Centrally Symmetric Polytopes

Abstract
The theory of toric varieties provides a fruitful link between combinatorial questions on convex polytopes and algebraic geometry. For example there is a beautiful characterization of the possible numbers of faces of a simplicial convex polytope due to P. McMullen, L. Billera, C. Lee and R. Stanley. Stanley could prove the necessity of the conditions by translating them into topological statements on the projective toric variety associated to the polytope.

In this talk, I will consider polytopes with a central symmetry, but not necessarily simplicial, and prove a lower bound for a certain combinatorial invariant, using intersection cohomology.

Contact person:Jørgen Ellegaard Andersen.