Diffeomorphisms, Isotopoies, and Braid Monodromy Factorizations of Plane Cuspidal Curves

Details Diffeomorphisms, Isotopoies, and Braid Monodromy Factorizations of Plane Cuspidal Curves Diffeomorphisms, Isotopoies, and Braid Monodromy Factorizations of Plane Cuspidal Curves

2001-04-02

arxiv.org/abs/math/0104021v2

Mathematics

Algebraic Geometry

Principal changement concerns the calculation of the number of double points and cups

Scientific paper

We prove that there is an infinite sequence of pairs of plane cuspidal curves $C_{m,1}$ and $C_{m,2}$, such that the pairs $(\Bbb CP^2, C_{m,1})$ and $(\Bbb CP^2, C_{m,2})$ are diffeomorphic, but $C_{m,1}$ and $C_{m,2}$ have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of "Dif=Def" and "Dif=Iso" problems for plane irreducible cuspidal curves. In our examples, $C_{m,1}$ and $C_{m,2}$ are complex conjugated.

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