English

On fundamental groups related to the Hirzebruch surface F_1

Algebraic Geometry 2015-05-13 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0706.1680,
  title  = {On fundamental groups related to the Hirzebruch surface F_1},
  author = {Michael Friedman and Mina Teicher},
  journal= {arXiv preprint arXiv:0706.1680},
  year   = {2015}
}

Comments

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