G. Dethloff and S. Lu .
Titre:
""Logarithmic Surfaces and Hyperbolicity".
Abstract : In 1981 J.Noguchi
proved that in a logarithmic algebraic manifold, having logarithmic irregularity
strictly bigger than its dimension, any entire curve is algebraically degenerate.
In the present paper we are interested in the case of manifolds having
logarithmic irregularity equal to its dimension. We restrict our attention to
Brody curves, for which we resolve the problem completely in dimension 2:
Theorem: In a logarithmic surface with logarithmic irregularity 2 and
logarithmic Kodaira dimension at least 1, any Brody curve is algebraically
degenerate.
As a corollary, we get hyperbolicity for such logarithmic surfaces not
containing non-hyperbolic algebraic curves and having hyperbolically stratified
boundary divisors. In particular we get the "best possible" result on
algebraic degeneracy of Brody curves in the complex plane minus a curve
consisting of three components, thus improving results of
Dethloff-Schumacher-Wong from 1995.