Dedekind sums and the signature of \(f(x,y)+z^N\)
type: Item
instance of: scholarly article
title: Dedekind sums and the signature of \(f(x,y)+z^N\)
zbMATH Open document ID: 0912.32029
author: András Némethi
published in: Selecta Mathematica. New Series
publication date: 1999-05-10T00:00:00Z
review text: There is a relatively long-standing conjecture of Durfee, stating that the signature of the Milnor fiber of an isolated complete intersection is negative. Even stronger, he conjectured the inequality \(p_g \leq \mu/6\), where \(p_g\) is the geometric genus, and \(\mu\) the Milnor number. In this paper the author proves this inequality for singularities of type \(f(x,y) + z^N,\) where \(f\) defines an irreducible plane curve singularity. Its proof uses generalized Dedekind sums associated to the embedded resolution of \(f\).
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 32S50
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 1206723
zbMATH Keywords: Milnor fiber
zbMATH Keywords: signature
zbMATH Keywords: eta invariant
zbMATH Keywords: Dedekind sums
zbMATH Keywords: singularities
MaRDI profile type: Publication
full work available at URL: s000290050035
OpenAlex ID: W1976437339
DOI: 10.1007/S000290050035
description: scientific article; zbMATH DE number 1206723