Topology of generic line arrangements

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.

Keywords

line arrangement, hyperplane arrangement, polynomial in several variables

2010 Mathematics Subject Classification

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

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Published 19 June 2015