%0 Journal Article %T On braid monodromy factorizations %A V. Kharlamov %A Vik. S. Kulikov %J Mathematics %D 2003 %I arXiv %R 10.1070/IM2003v067n03ABEH000436 %X 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. %U http://arxiv.org/abs/math/0302113v1