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

Ito, Atsushi; Tiba, Yusaku

Annales de l'Institut Fourier, Tome 65 (2015) no. 5, pp. 2057-2068.

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.

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.

Classification : 32Q45, 14J26
Keywords: Kobayashi hyperbolic imbedding, holomorphic map
Mot clés : Plongement Kobayashi-hyperbolique, application holomorphes

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