Advanced Studies in Pure Mathematics

On the middle Betti number of certain singularities with critical locus a hyperplane

Mamuka Shubladze

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Abstract

We study holomorphic germs $f : (\mathbb{C}^{n+1}, 0) \to (\mathbb{C}, 0)$ with the following properties:

(i) the critical set $H$ of the germ $f$ is a hyperplane $H = \{x = 0\}$;

(ii) the transversal singularity of the germ $f$ in points of the set $H \setminus \{0\}$ has type $A_{k-1}$.

We will investigate the topological structure of the Milnor fibre for $f$ and give explicit formula for the middle Betti number of the Milnor fibre and for the quasihomogeneous case we express it in terms of weights and degrees.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 303-320

Dates
Received: 28 March 2008
Revised: 26 December 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448023

Digital Object Identifier
doi:10.2969/aspm/05610303

Mathematical Reviews number (MathSciNet)
MR2604088

Zentralblatt MATH identifier
1197.57029

Subjects
Primary: 57R45: Singularities of differentiable mappings

Keywords
Non-isolated singularity Milnor fibration Milnor number

Citation

Shubladze, Mamuka. On the middle Betti number of certain singularities with critical locus a hyperplane. Singularities — Niigata–Toyama 2007, 303--320, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610303. https://projecteuclid.org/euclid.aspm/1543448023


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