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 Nklt(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.
Hyperbolicity for log canonical pairs and the cone theorem / R. Svaldi. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - 25:5(2019). [10.1007/s00029-019-0512-9]
Hyperbolicity for log canonical pairs and the cone theorem
R. Svaldi
2019
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 Nklt(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.File | Dimensione | Formato | |
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