Remarks on Laufer's formula for the Milnor number, Rochlin's signature theorem and the analytic Euler characteristic of compact complex manifolds
type: Item
instance of: scholarly article
title: Remarks on Laufer's formula for the Milnor number, Rochlin's signature theorem and the analytic Euler characteristic of compact complex manifolds
zbMATH Open document ID: 1384.32022
published in: Methods and Applications of Analysis
publication date: 2018-01-10T00:00:00Z
review text: Isolated hypersurface singularities \((V,0)\) defined by germs of holomorphic mappings \(f:(\mathbb{C}^{n+1},0)\rightarrow (\mathbb{C},0)\) can be studied using resolution of singularities \(\pi :\tilde{V}\rightarrow V\) or by considering the way noncritical levels of \(f\) degenerate to the special fiber of \(V\). Laufer's formula establishes a bridge between these two viewpoints. It says that for \(n=3\), one has \(\mu +1=\chi (\tilde{V})+K^2+12\rho _g\), where \(\mu\) is the Milnor number, \(\chi\) is the Euler characteristic, \(K^2\) is the self-intersection number of the canonical class of the resolution, and \(\rho _g\) is the geometric genus. In the paper this formula is considered in relationship with Gorenstein surface singularities and Rochlin's signature theorem.
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 32S55
zbMATH DE Number: 6823590
zbMATH Keywords: Gorenstein surface singularities
zbMATH Keywords: Rochlin invariant
zbMATH Keywords: Milnor number
author: José Seade
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
DOI: 10.4310/MAA.2017.V24.N1.A8
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description: scientific article; zbMATH DE number 6823590