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Bifurcation braid monodromy of plane curves

Title data

Lönne, Michael:
Bifurcation braid monodromy of plane curves.
In: Ebeling, Wolfgang ; Hulek, Klaus ; Smoczyk, Knut (ed.): Complex and Differential Geometry : Conference held at Leibniz Universität Hannover, September 14 – 18, 2009. - Berlin : Springer , 2011 . - pp. 235-255 . - (Springer Proceedings in Mathematics ; 8 )
ISBN 978-3-642-20299-5
DOI: https://doi.org/10.1007/978-3-642-20300-8_14

Abstract in another language

We consider spaces of plane curves in the setting of algebraic geometry and of singularity theory. On one hand there are the complete linear systems, on the other we consider unfolding spaces of bivariate polynomials of Brieskorn-Pham type. For suitable open subspaces we can define the bifurcation braid monodromy taking values in the Zariski resp. Artin braid group. In both cases we give the generators of the image. These results are compared with the corresponding geometric monodromy. It takes values in the mapping class group of braided surfaces. Our final result gives a precise statement about the interdependence of the two monodromy maps. Our study concludes with some implication with regard to the unfaithfulness of the geometric monodromy ([W]) and the – yet unexploited – knotted geometric monodromy, which takes the ambient space into account.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: braid monodromy; plane algebraic curves
Subject classification: Mathematics Subject Classification Code: 32S50 14D05 32S55 57Q45
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 23 Nov 2021 13:49
Last Modified: 23 Nov 2021 14:37
URI: https://eref.uni-bayreuth.de/id/eprint/67987