Curves in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded

[Courbes complexes dans des surfaces quadriques et cubiques à complémentaire Kobayashi-hyperbolique]

Ito, Atsushi ; Tiba, Yusaku

Annales de l'Institut Fourier, Tome 65 (2015), p. 2057-2068 / Harvested from Numdam

Résumé

Nous construisons des courbes complexes lisses de degré minimal possible dans des surfaces quadriques et cubiques à complémentaire hyperboliquement plongé, au sens de Kobayashi. De plus, nous caractérisons les fibrés en droites sur de telles surfaces dont les systèmes linéaires associés possèdent des courbes lisses à complémentaire hyperboliquement plongé.

Abstract

We construct smooth irreducible curves of the lowest possible degrees in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded into those surfaces. Moreover we characterize line bundles on quadric and cubic surfaces such that the complete linear systems of the line bundles have a smooth irreducible curve whose complement is Kobayashi hyperbolically imbedded into those surfaces.

Détail

Publié le : 2015-01-01

Zbl 06541628

DOI : https://doi.org/10.5802/aif.2982
Classification:  32Q45,  14J26
Mots clés: Plongement Kobayashi-hyperbolique, application holomorphes

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