Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 4

Special Issue: In Honor of Prof. Gert-Martin Greuel’s 75th Birthday

Guest Editors: Igor Burban, Stanislaw Janeczko, Gerhard Pfister, Stephen S.T. Yau, and Huaiqing Zuo

Connectedness of Milnor fibres and Stein factorization of compactifiable holomorphic functions

Pages: 1083 – 1098

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n4.a8


Helmut A. Hamm (Mathematisches Institut, Universität Münster, Germany)


We start with conditions under which the Milnor fibre of a holomorphic function on a singular space is connected. In this case the special fibre is contractible, hence connected. So we pass to a more general question: compare the number of connected components of the fibres of a holomorphic function. Useful ingredients are local Lefschetz theorems and some kind of a Stein factorization.

2010 Mathematics Subject Classification

Primary 32S55. Secondary 14B05, 32S50.

Received 4 January 2019

Accepted 18 October 2019

Published 13 November 2020