2010/03/15 by Michael Lönne, Lönne, Michael
Mathematics · Physics and Astronomy · #32S50 (14D05 32S55 57Q45) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1003.3044
openalex publication_date 2010/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 and the - yet unexploited - knotted geometric monodromy, which takes the ambient space into account.