Remarks on the positivity of the cotangent bundle of a K3 surface
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909787221917696 |
|---|---|
| author | Gounelas, Frank Ottem, John Christian |
| author_facet | Gounelas, Frank Ottem, John Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_09598 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Remarks on the positivity of the cotangent bundle of a K3 surface Gounelas, Frank Ottem, John Christian Algebraic Geometry 14J28, 14C20, 14J42 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. |
| title | Remarks on the positivity of the cotangent bundle of a K3 surface |
| topic | Algebraic Geometry 14J28, 14C20, 14J42 |
| url | https://arxiv.org/abs/1806.09598 |