  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 $p\neq q$.
