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Braid Monodromy of some Brieskorn-Pham Singularities

Title data

Lönne, Michael:
Braid Monodromy of some Brieskorn-Pham Singularities.
In: International Journal of Mathematics. Vol. 21 (2010) Issue 8 . - pp. 1047-1070.
ISSN 1793-6519
DOI: https://doi.org/10.1142/S0129167X10006379

Abstract in another language

For germs of isolated hypersurface singularities Lyashko and Looijenga introduced a map LL on the complement of the bifurcation set. It takes values in the space of simple polynomials of degree equal to the Milnor number μ of the singularity, and thus induces a map LL* from the fundamental group to the braid group on μ strands.

For the case of curve singularities given by a polynomial x3 + yℓ+1 we give a uniform description of the image LL* and derive a presentation of the discriminant knot group, i.e. for the fundamental group of the complement to the discriminant divisor.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: hypersurface singularities; versal unfolding; Dynkin diagram; braid monodromy; discriminant knot group
Subject classification: Mathematics Subject Classification Code: 32S40 32S25 14D05 20F36
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors > Professorship Algebraic Geometry - apl. Prof. Dr. Michael Lönne
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 23 Nov 2021 14:32
Last Modified: 15 Sep 2022 07:46
URI: https://eref.uni-bayreuth.de/id/eprint/67991