Topology of generic line arrangements
Geometric Topology
2012-06-27 v2
Abstract
Our aim is to generalize the result that two generic complex line arrangements are equivalent. In fact for a line arrangement A we associate its defining polynomial, the product of a_ix+b_iy+c_i, so that A = (f=0). We prove that the defining polynomials of two generic line arrangements are, up to a small deformation, topologically equivalent. In higher dimension the related result is that within a family of equivalent hyperplane arrangements the defining polynomials are topologically equivalent.
Keywords
Cite
@article{arxiv.1205.2203,
title = {Topology of generic line arrangements},
author = {Arnaud Bodin},
journal= {arXiv preprint arXiv:1205.2203},
year = {2012}
}
Comments
This second version is the first half of v1, that has been been split in two parts for clarity (The second part will be post soon.) The main result has been generalized to generic line arrangements, allowing parallel lines