Geodesic
Remarks on the positivity of the cotangent bundle of a K3 surface
Épijournal de Géométrie Algébrique, Tome 4 (2020)

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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. 
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     title = {Remarks on the positivity of the cotangent bundle of a {K3} surface},
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Gounelas, Frank; Ottem, John Christian. Remarks on the positivity of the cotangent bundle of a K3 surface. Épijournal de Géométrie Algébrique, Tome 4 (2020). doi: 10.46298/epiga.2020.volume4.5924

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