Remarks on the positivity of the cotangent bundle of a K3 surface
Authors: Frank Gounelas ; John Christian Ottem
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Frank Gounelas;John Christian Ottem
Using recent results of Bayer-Macrì, 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.
Anella, Fabrizio; Höring, Andreas, 2021, Twisted Cotangent Bundle Of Hyperkähler Manifolds (With An Appendix By Simone Diverio), Journal De l’École Polytechnique — Mathématiques, 8, pp. 1429-1457, 10.5802/jep.175.
Dutta, Yajnaseni; Huybrechts, Daniel, 2022, Maximal Variation Of Curves On K3 Surfaces, Tunisian Journal Of Mathematics, 4, 3, pp. 443-464, 10.2140/tunis.2022.4.443.