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.
- Holomorphic map
- Kobayashi hyperbolic imbedding
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology