Geodesic
On braid monodromy factorizations
Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 499-534

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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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     author = {V. M. Kharlamov and Vik. S. Kulikov},
     title = {On braid monodromy factorizations},
     journal = {Izvestiya. Mathematics },
     pages = {499--534},
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     volume = {67},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a4/}
}
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V. M. Kharlamov; Vik. S. Kulikov. On braid monodromy factorizations. Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 499-534. http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a4/