Braid Monodromy Factorization and Diffeomorphism Types

Details Braid Monodromy Factorization and Diffeomorphism Types Braid Monodromy Factorization and Diffeomorphism Types

1999-05-20

arxiv.org/abs/math/9905129v1

Mathematics

Algebraic Geometry

2 files: TEX file of text and file of figures (gzipped)

Scientific paper

In this manuscript we prove that if two cuspidal plane curves have equivalent braid monodromy factorizations, then they are smoothly isotopic in the plane. As a consequence of this and the Chisini conjecture, we obtain that if two discriminant curves (or branch curves in other terminology) of generic projections (to the plane) of surfaces of general type imbedded in a projective space by means of a multiple canonical class have equivalent braid monodromy factorizations, then the surfaces are diffeomorphic (if we consider them as real 4-folds).

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