On fundamental groups related to the Hirzebruch surface F_1

Details On fundamental groups related to the Hirzebruch surface F_1 On fundamental groups related to the Hirzebruch surface F_1

2007-06-12

arxiv.org/abs/0706.1680v1

Mathematics

Algebraic Geometry

accepted for publication at "Sci. in China, ser. Math"; 22 pages, 11 figures

Scientific paper

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C^2 or in CP^2. In this article, we show that these groups, for the Hirzebruch surface F_{1,(a,b)}, are almost-solvable. That is - they are an extension of a solvable group, which strengthen the conjecture on degeneratable surfaces.

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