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.
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.
Keywords: Kobayashi hyperbolic imbedding, holomorphic map
Mot clés : Plongement Kobayashi-hyperbolique, application holomorphes
@article{AIF_2015__65_5_2057_0, author = {Ito, Atsushi and Tiba, Yusaku}, title = {Curves in quadric and cubic surfaces whose complements are {Kobayashi} hyperbolically imbedded}, journal = {Annales de l'Institut Fourier}, pages = {2057--2068}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {5}, year = {2015}, doi = {10.5802/aif.2982}, zbl = {06541628}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2982/} }
TY - JOUR AU - Ito, Atsushi AU - Tiba, Yusaku TI - Curves in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded JO - Annales de l'Institut Fourier PY - 2015 SP - 2057 EP - 2068 VL - 65 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2982/ DO - 10.5802/aif.2982 LA - en ID - AIF_2015__65_5_2057_0 ER -
%0 Journal Article %A Ito, Atsushi %A Tiba, Yusaku %T Curves in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded %J Annales de l'Institut Fourier %D 2015 %P 2057-2068 %V 65 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2982/ %R 10.5802/aif.2982 %G en %F AIF_2015__65_5_2057_0
Ito, Atsushi; Tiba, Yusaku. Curves in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded. Annales de l'Institut Fourier, Volume 65 (2015) no. 5, pp. 2057-2068. doi : 10.5802/aif.2982. http://archive.numdam.org/articles/10.5802/aif.2982/
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