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Archiv der Mathematik

, Volume 87, Issue 3, pp 217–226 | Cite as

On toric h-vectors of centrally symmetric polytopes

  • Annette A’Campo–Neuen
Original Paper

Abstract.

We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational.

Mathematics Subject Classification (2000).

52B12 52B05 14M25 14F43 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BaselBaselSwitzerland

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