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