Arrangements of double pseudolines

Abstract

Define an arrangement of double pseudolines as a finite family of at least two separating simple closed curves embedded in a projective plane, with the property that any two meet transversally in exactly four points and induce a cell structure on the projective plane. We show that any arrangement of double pseudolines is isomorphic to the dual family of a finite family of pairwise disjoint convex bodies of a projective plane endowed with a topological point-line incidence geometry and we provide a simple axiomatic characterization of the class of isomorphism classes of indexed arrangements of oriented double pseudolines.