Bernoulli moments of spectral numbers and Hodge numbers

2004/05/26 by Thomas Brélivet, Brélivet, Thomas, Claus Hertling +1
Mathematics · #32S25 #32S35 #62E99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:32S25 #msc:32S35 #msc:62E99

paper · pdf · doi:10.48550/arxiv.math/0405501

35 pages, 2 figures

arxiv created 2004/05/26 · openalex publication_date 2004/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The distribution of the spectral numbers of an isolated hypersurface singularity is studied in terms of the Bernoulli moments. These are certain rational linear combinations of the higher moments of the spectral numbers. They are related to the generalized Bernoulli polynomials. We conjecture that their signs are alternating and prove this in many cases. One motivation for the Bernoulli moments comes from the comparison with compact complex manifolds.

Citations

• On Betti numbers and Chern classes of varieties with trivial odd cohomology groups
• Elliptic Gromov - Witten invariants and the generalized mirror\n conjecture

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• A Hodge index for Grothendieck residue pairing
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• Ramanujan-Bernoulli numbers as moments of Racah polynomials