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

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

1997-03-19

arxiv.org/abs/alg-geom/9703023v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $p\neq q$.

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