## Frank Gounelas ; John Christian Ottem - Remarks on the positivity of the cotangent bundle of a K3 surface

epiga:5924 - Épijournal de Géométrie Algébrique, June 23, 2020, Volume 4 - https://doi.org/10.46298/epiga.2020.volume4.5924
Remarks on the positivity of the cotangent bundle of a K3 surface

Authors: 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.

Volume: Volume 4
Published on: June 23, 2020
Accepted on: June 23, 2020
Submitted on: November 28, 2019
Keywords: Mathematics - Algebraic Geometry,14J28, 14C20, 14J42