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Braid monodromy factorizations and diffeomorphism types

Vik. S. Kulikov^a, M. Teicher<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences
^b Bar-Ilan University, Department of Chemistry

Abstract: 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).

MSC: 14E20

Received: 29.12.1998

DOI: 10.4213/im285

 English version: Izvestiya: Mathematics, 2000, 64:2, 311–341

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