Plane Curves with Hyperbolic and C{hyperbolic Complements


We nd suucient conditions for the complement IP 2 n C of a plane curve C to be C{hyperbolic. The latter means that some covering over IP 2 n C is Carath eodory hyperbolic. This implies that this complement IP 2 n C is Kobayashi hyperbolic, and (due to Lin's Theorem) the fundamental group 1 (IP 2 nC) does not contain a nilpotent subgroup of nite index. We… (More)