Asian Journal of Mathematics

Volume 19 (2015)

Number 3

Topology of generic line arrangements

Pages: 377 – 390



Arnaud Bodin (Laboratoire Paul Painlevé, Mathématiques, Université Lille 1, Villeneuve d’Ascq, France )


Our aim is to generalize the result that two generic complex line arrangements are equivalent. In fact for a line arrangement $\mathcal{A}$ we associate a defining polynomial $f = \prod_i (a_i x + b_i y + c_i)$, so that $\mathcal{A} = (f = 0)$. 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.


line arrangement, hyperplane arrangement, polynomial in several variables

2010 Mathematics Subject Classification

Primary 32S22. Secondary 14N20, 32S15, 57M25.

Published 19 June 2015