Hyperbolicity for log canonical pairs and the cone theorem

Roberto Svaldi ^[1]
1. [1] École polytechnique fédérale de Lausanne ‐ EPFL, Suiza
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 5, 2019
Idioma: inglés
DOI: 10.1007/s00029-019-0512-9
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Resumen
- Given a log canonical pair (X,Δ), we show that KX+Δ 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,Δ). This implies a generalization of the Cone Theorem where each KX+Δ-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 Nklt(X,Δ). Moreover, we give a criterion of Nakai type to determine when under the above condition KX+Δ is ample and we prove some partial results in the case of arbitrary singularities.