On braid monodromy factorizations

Details On braid monodromy factorizations On braid monodromy factorizations

2003-02-11

arxiv.org/abs/math/0302113v1

Mathematics

Algebraic Geometry

52 pages, AMS-TeX

Scientific paper

We introduce and develop a language of semigroups over the braid groups for a study of braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application we give a new proof of Orevkov's theorem on realization of a bmf over a disc by algebraic curves and show that the complexity of such a realization can not be bounded in terms of the types of the factors of the bmf. Besides, we prove that the type of a bmf is distinguishing Hurwitz curves with singularities of inseparable types up to $H$-isotopy and $J$-holomorphic cuspidal curves in $\C P^2$ up to symplectic isotopy.

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