A note on hyperbolicity for log canonical pairs

R. Svaldi

Published 2014-10-09Version 1

Given a log canonical pair $(X, \Delta)$, we prove that $K_X+\Delta$ is nef assuming there is no non constant map from the projective line with values in the open strata of the stratification induced by the non klt locus of $\Delta$. This implies a generalization of the Cone Theorem. Moreover, we give a criterion of Nakai type to determine when under the above condition $K_X+\Delta$ is ample. We prove some partial results in the case of arbitrary singularities.