Braid monodromy factorizations and diffeomorphism types

Vik. S. Kulikov ; M. Teicher

Izvestiya. Mathematics , Tome 64 (2000) no. 2, pp. 311-341

Résumé

In this paper we prove that if two cuspidal plane curves $B_1$ and $B_2$ have equivalent braid monodromy factorizations, then $B_1$ and $B_2$ are smoothly isotopic in $\mathbb C\mathbb P^2$. As a consequence, we obtain that if $S_1$, $S_2$ are surfaces of general type embedded in a projective space by means of a multiple canonical class and if the discriminant curves (the branch curves) $B_1$, $B_2$ of some smooth projections of $S_1$, $S_2$ to $\mathbb{CP}^2$ have equivalent braid monodromy factorizations, then $S_1$ and $S_2$ are diffeomorphic (as real four-dimensional manifolds).