Plane Curves with Hyperbolic and C-hyperbolic Complements

Abstract

The general problem which initiated this work is: What are the quasiprojective varieties which can be uniformized by means of bounded domains in $\cz^n$ ? Such a variety should be, in particular, C--hyperbolic, i.e. it should have a Carathéodory hyperbolic covering. We study here the plane projective curves whose complements are C--hyperbolic. For instance, we show that most of the curves whose duals are nodal or, more generally, immersed curves, belong to this class. We also give explicit examples of irreducible such curves of any even degree d greater or equal 6.

Final version, published in 1996, subsuming version 1 of this preprint and another work by the same authors on "Examples of Plane Curves with Hyperbolic and C-hyperbolic Complements"