On a discriminant knot group problem of Brieskorn

Michael Lönne

Journal of Singularities
volume 18 (2018), 455-463

Received: 31 December 2017. Accepted: 7 April 2018.

DOI: 10.5427/jsing.2018.18x

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Abstract:

Quite some time ago, at the singularity conference at Cargèse 1972, Brieskorn asked the following question: "Is the local fundamental group π_1^s(S-D) of the discriminant complement inside the semi-universal unfolding S of an isolated hypersurface singularity constant for s in the μ-constant stratum Σ_E?" We review this question and give an affirmative answer in case of singular plane curve germs of multiplicity at most 3.


Keywords:

plane curve singularity, discriminant knot group, μ-constant stratum, braid monodromy


Mathematical Subject Classification:

32S50 primary, 14D05, 32S55, 20F36 secondary


Author(s) information:

Michael Lönne
Mathematik VIII
Universität Bayreuth
Universitätstrasse 30
95447 Bayreuth, Germany
email: michael.loenne@uni-bayreuth.de