On Betti numbers and Chern classes of varieties with trivial odd cohomology groups

Abstract

It was noticed in a very recent preprint of T. Eguchi, K. Hori, and Ch.-Sh. Xiong (hep-th/9703086) that a curious identity between Betti numbers and Chern classes holds for many examples of Fano varieties. The goal of this paper is to prove that for varieties with trivial odd cohomology groups this identity is equivalent to having zero Hodge numbers $h^{p,q}$ for $p\ne q$.

5 pages, LaTeX. It turned out that most of the results of the paper are already known. The appropriate reference is added

References in corpus (1)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

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