Quasiprojective varieties admitting Zariski dense entire holomorphic curves

Abstract

Let X be a complex quasiprojective variety. A result of Noguchi–Winkelmann–Yamanoi shows that if X admits a Zariski dense entire curve, then its quasi-Albanese map is a fiber space. We show that the orbifold structure induced by a proper birationally equivalent map on the base is special in this case. As a consequence, if X is of log-general type with q(X)dimX, then any entire curve is contained in a proper subvariety in X.