Topology of generic line arrangements

2012/05/10 by Bodin, Arnaud
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1205.2203

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.

Related

• Topological line arrangements and their topological invariants
• Topology of hyperplane arrangements via real structure
• Topology and combinatorics of real line arrangements
• Non-very generic arrangements in low dimension
• Arithmetic non-very generic arrangements