关于K3曲面的余切束正性的注释

IF 0.9 Q2 MATHEMATICS Epijournal de Geometrie Algebrique Pub Date : 2018-06-25 DOI:10.46298/epiga.2020.volume4.5924

Frank Gounelas, J. C. Ottem

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引用次数: 12

摘要

利用Bayer-Macr\ ' i的最新结果，我们在许多情况下计算了光滑投影K3曲面的投影余切束的伪有效锥和伪有效锥。然后，我们使用这些结果来构造光滑曲线的显式族，在这些光滑曲线上，余切束的限制不是半稳定的(因此不是nef)。特别是，这导致了坎帕纳-彼得内尔问题的反例。评论:已发布版本

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Remarks on the positivity of the cotangent bundle of a K3 surface

Using recent results of Bayer-Macr\`i, we compute in many cases the pseudoeffective and nef cones of the projectivised cotangent bundle of a smooth projective K3 surface. We then use these results to construct explicit families of smooth curves on which the restriction of the cotangent bundle is not semistable (and hence not nef). In particular, this leads to a counterexample to a question of Campana-Peternell. Comment: Published version

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