Weak analytic hyperbolicity of generic hypersurfaces of high degree in ℙ 4

Erwan Rousseau[1]

  • [1] Département de Mathématiques, IRMA, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg, France.

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 2, page 369-383
  • ISSN: 0240-2963

Abstract

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In this article we prove that every entire curve in a generic hypersurface of degree d ≥ 593 in ℙ ℂ 4 is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.

How to cite

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Rousseau, Erwan. "Weak analytic hyperbolicity of generic hypersurfaces of high degree in $\mathbb{P}^{4}$." Annales de la faculté des sciences de Toulouse Mathématiques 16.2 (2007): 369-383. <http://eudml.org/doc/10055>.

@article{Rousseau2007,
abstract = {In this article we prove that every entire curve in a generic hypersurface of degree $d\ge 593$ in $\{\mathbb\{P\}\}_\{\mathbb\{C\}\}^\{4\}$ is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.},
affiliation = {Département de Mathématiques, IRMA, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg, France.},
author = {Rousseau, Erwan},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {hyperbolic manifold; entire curves; jet differentials; Kobayashi conjecture; hypersurfaces},
language = {eng},
number = {2},
pages = {369-383},
publisher = {Université Paul Sabatier, Toulouse},
title = {Weak analytic hyperbolicity of generic hypersurfaces of high degree in $\mathbb\{P\}^\{4\}$},
url = {http://eudml.org/doc/10055},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Rousseau, Erwan
TI - Weak analytic hyperbolicity of generic hypersurfaces of high degree in $\mathbb{P}^{4}$
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 2
SP - 369
EP - 383
AB - In this article we prove that every entire curve in a generic hypersurface of degree $d\ge 593$ in ${\mathbb{P}}_{\mathbb{C}}^{4}$ is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.
LA - eng
KW - hyperbolic manifold; entire curves; jet differentials; Kobayashi conjecture; hypersurfaces
UR - http://eudml.org/doc/10055
ER -

References

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  8. Kobayashi (S.).— Hyperbolic manifolds and holomorphic mappings, Marcel Dekker, New York (1970). Zbl0207.37902MR277770
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  10. Paun (M.).— Vector fields on the total space of hypersurfaces in the projective space and hyperbolicity, preprint (2005). 
  11. Rousseau (E.).— Etude des jets de Demailly-Semple en dimension 3, Ann. Inst. Fourier, 56, p. 397-421 (2006). Zbl1092.58003MR2226021
  12. Rousseau (E.).— Equations différentielles sur les hypersurfaces de ℙ 4 , to appear in J. Math. Pures Appl. (2006). Zbl1115.14009MR2257847
  13. Siu (Y.-T.).— Hyperbolicity in complex geometry, The legacy of Niels Henrik Abel, Springer, Berlin, p. 543-566 (2004). Zbl1076.32011MR2077584
  14. Voisin (C.).— On a conjecture of Clemens on rational curves on hypersurfaces, J. Diff. Geom., 44, p. 200-213 (1996). Zbl0883.14022MR1420353

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