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

1997/03/19 by Lev Borisov, Borisov, Lev A. · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.alg-geom/9703023

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≠ q.

Citations

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

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• Global spectra, polytopes and stacky invariants
• Variance of the exponents of orbifold Landau-Ginzburg models
• Bernoulli moments of spectral numbers and Hodge numbers

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