Bernoulli moments of spectral numbers and Hodge numbers

Thomas Brélivet and Claus Hertling

Journal of Singularities
volume 20 (2020), 205-231

Received: 5 February 2019. Received in revised form: 7 April 2020

DOI: 10.5427/jsing.2020.20i

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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 fo the Bernoulli moments comes from the analogy with compact complex manifolds.

2010 Mathematical Subject Classification:

32S25, 62E99, 32S35

Key words and phrases:

Spectral numbers, Bernoulli polynomials, higher moments, singularities

Author(s) information:

Thomas Brélivet	Claus Hertling
	Chair for Algebraic Geometry
	University Mannheim, B6, 26
	68159 Mannheim, Germany
email: thomas.brelivet@gmail.com	email: dhertling@math.uni-mannheim.de