Hyperbolicity for log canonical pairs and the cone theorem

DOI10.1007/S00029-019-0512-9zbMATH Open1442.14057arXiv1410.2529OpenAlexW2981997643MaRDI QIDQ2334608

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Publication date: 7 November 2019

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Abstract: Given a log canonical pair $(X,Delta)$, we show that $K_X+Delta$ is nef assuming there is no non-constant map from the affine line with values in the open strata of the stratification induced by the non-klt locus of $(X,Delta)$. This implies a generalization of the Cone Theorem where each $K_X+Delta$-negative extremal ray is spanned by a rational curve that is the closure of a copy of the affine line contained in one of the open strata of $mathrmNklt(X,Delta)$. Moreover, we give a criterion of Nakai type to determine when under the above condition $K_X+Delta$ is ample and we prove some partial results in the case of arbitrary singularities.

Full work available at URL: https://arxiv.org/abs/1410.2529

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