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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Bifurcation braid monodromy of plane curves
verfasst von : Michael Lönne
Erschienen in: Complex and Differential Geometry
Verlag: Springer Berlin Heidelberg
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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.