Degeneracy of holomorphic curves into algebraic varieties

Applying the Second Main Theorem of [J. Noguchi, J. Winkelmann, K. Yamanoi, The second main theorem for holomorphic curves into semi-Abelian varieties II, Forum Math., in press, e-print archive, math. CV/0405492], we deal with the algebraic degeneracy of entire holomorphic curves f : C -> X from the complex plane C into a complex algebraic normal variety X of positive log Kodaira dimension that admits a finite proper morphism to a semi-Abelian variety. We will also discuss applications to the Kobayashi hyperbolicity problem. (C) 2007 Published by Elsevier Masson SAS.