ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 52 B 05, 14 M 25 Altmann, Klaus, Humboldt-University Berlin Hodge numbers for polytopes For any compact polytope P, Danilov has defined numbers h^{i,j}(P) reflecting the combinatorics of P. In case P is rational, they equal the Hodge numbers of the corresponding projective toric variety. As a second application, we discuss the relation of these polytopal Hodge numbers to deformation theory and present a vanishing theorem for h^{1,2}.