On braid monodromy factorizations

V. M. Kharlamov ; Vik. S. Kulikov

Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 499-534.

Résumé

We introduce and develop a language of semigroups over the braid groups to study the 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 the realization of bmf's over a disc by algebraic curves and show that the complexity of such a realization cannot be bounded in terms of the types of factors of the bmf. We also prove that the type of a bmf distinguishes Hurwitz curves with singularities of inseparable type up to $H$-isotopy and $J$-holomorphic cuspidal curves in $\mathbb{CP}^2$ up to symplectic isotopy.

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