In this article we prove that every entire curve in a generic hypersurface of degree in is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.
Dans cet article nous démontrons que toute courbe entière dans une hypersurface générique de degré dans est algébriquement dégénérée i.e il existe une sous-variété propre qui contient la courbe entière.
@article{AFST_2007_6_16_2_369_0, author = {Rousseau, Erwan}, title = {Weak analytic hyperbolicity of generic hypersurfaces of high degree in $\mathbb{P}^{4}$}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {369--383}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 16}, number = {2}, year = {2007}, doi = {10.5802/afst.1152}, mrnumber = {2331545}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1152/} }
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 SP - 369 EP - 383 VL - 16 IS - 2 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1152/ DO - 10.5802/afst.1152 LA - en ID - AFST_2007_6_16_2_369_0 ER -
%0 Journal Article %A Rousseau, Erwan %T Weak analytic hyperbolicity of generic hypersurfaces of high degree in $\mathbb{P}^{4}$ %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2007 %P 369-383 %V 16 %N 2 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1152/ %R 10.5802/afst.1152 %G en %F AFST_2007_6_16_2_369_0
Rousseau, Erwan. Weak analytic hyperbolicity of generic hypersurfaces of high degree in $\mathbb{P}^{4}$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 2, pp. 369-383. doi : 10.5802/afst.1152. http://archive.numdam.org/articles/10.5802/afst.1152/
[1] Bogomolov (F.A.).— Holomorphic tensors and vector bundles on projective varieties, Math. USSR Izvestija 13, p. 499-555 (1979). | Zbl
[2] Clemens (H.).— Curves on generic hypersurface, Ann. Sci. Ec. Norm. Sup., 19, p. 629-636 (1986). | Numdam | MR | Zbl
[3] Demailly (J.-P.).— Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials, Proc. Sympos. Pure Math., vol.62, Amer. Math.Soc., Providence, RI, p.285-360 ( 1997). | MR | Zbl
[4] Demailly (J.-P.), El Goul J..— Hyperbolicity of generic surfaces of high degree in projective 3-space, Amer. J. Math 122, p. 515-546 (2000). | MR | Zbl
[5] Ein (L.).— Subvarieties of generic complete intersections, Invent. Math., 94, p. 163-169 (1988). | MR | Zbl
[6] Fulton (W.).— Intersection theory, Springer-Verlag, Berlin (1998). | MR | Zbl
[7] Green (M.), Griffiths P..— Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979, Proc. Inter. Sympos. Berkeley, CA, 1979, Springer-Verlag, New-York, p. 41-74 (1980). | MR | Zbl
[8] Kobayashi (S.).— Hyperbolic manifolds and holomorphic mappings, Marcel Dekker, New York (1970). | MR | Zbl
[9] McQuillan (M.).— Diophantine approximations and foliations, in Publ. Math. IHES (1998). | Numdam | MR | Zbl
[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). | Numdam | MR | Zbl
[12] Rousseau (E.).— Equations différentielles sur les hypersurfaces de , to appear in J. Math. Pures Appl. (2006). | MR | Zbl
[13] Siu (Y.-T.).— Hyperbolicity in complex geometry, The legacy of Niels Henrik Abel, Springer, Berlin, p. 543-566 (2004). | MR | Zbl
[14] Voisin (C.).— On a conjecture of Clemens on rational curves on hypersurfaces, J. Diff. Geom., 44, p. 200-213 (1996). | MR | Zbl
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