Quasiprojective varieties admitting Zariski dense entire
holomorphic curves

Steven S. Y. Lu; Jörg Winkelmann

doi:10.1515/form.2011.069

Article

Quasiprojective varieties admitting Zariski dense entire holomorphic curves

Steven S. Y. Lu and Jörg Winkelmann

Published/Copyright: February 25, 2012

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From the journal Volume 24 Issue 2

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.

Keywords.: Entire curve; special variety; quasiprojective variety

Received: 2009-07-15

Revised: 2010-05-04

Published Online: 2012-02-25

Published in Print: 2012-March

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Articles in the same Issue

https://doi.org/10.1515/form.2011.069

Keywords for this article

Entire curve; special variety; quasiprojective variety