Quasiprojective varieties admitting Zariski dense entire holomorphic curves

Steven S. Y. Lu, Jörg Winkelmann
2012 Forum mathematicum  
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 N q.X/ dim X, then any entire curve is contained in a proper subvariety in X.
doi:10.1515/form.2011.069 fatcat:yowsafoy35cqhpcbde6lzitz3i