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.