  The paper is a contribution to the conjecture of Kobayashi that the
complement of a generic curve in the projective plane is hyperbolic, provided
the degree is at least five. Previously the authors treated the cases of two
quadrics and a line and three quadrics. The main results are Let C be the union
of three curves in P_2 whose degrees are at least two, one of which is at least
three. Then for generic such configurations the complement of C is hyperbolic
and hyperbolically embedded. The same statement holds for complements of curves
in generic hypersurfaces X of degree at least five and curves which are
intersections of X with hypersurfaces of degree at least five. Furthermore
results are shown for curves on surfaces with picard number one.
