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 surfaceArticle

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
    Funding:
      Source : OpenAIRE Graph
    • Moduli of Crystals and K3 Surfaces; Funder: European Commission; Code: 681838

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