Non-deformability of entire curves in projective hypersurfaces of high degree
Annales de l'Institut Fourier, Volume 56 (2006) no. 1, p. 247-253
In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree d2n in the complex projective space n . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.
Dans cet article, nous démontrons qu’il n’existe pas de famille de rang maximal de courbes entières dans la famille universelle des hypersurfaces de degré d2n dans l’espace projectif complexe n . Cela peut se voir comme une version faible de la conjecture de Kobayashi affirmant qu’une hypersurface projective générale de haut degré est hyperbolique au sens de Kobayashi.
DOI : https://doi.org/10.5802/aif.2178
Classification:  14J70,  32Q45
Keywords: projective hypersurfaces, entire curves, Kobayashi hyperbolicity
@article{AIF_2006__56_1_247_0,
     author = {Debarre, Olivier and Pacienza, Gianluca and P\u aun, Mihai},
     title = {Non-deformability of entire curves in projective hypersurfaces of high degree},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {1},
     year = {2006},
     pages = {247-253},
     doi = {10.5802/aif.2178},
     zbl = {1096.32010},
     mrnumber = {2228686},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2006__56_1_247_0}
}
Non-deformability of entire curves in projective hypersurfaces of high degree. Annales de l'Institut Fourier, Volume 56 (2006) no. 1, pp. 247-253. doi : 10.5802/aif.2178. https://aif.centre-mersenne.org/item/AIF_2006__56_1_247_0/

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