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Sur la conjecture de Kobayashi et l'hyperbolicité des hypersurfaces projectives en dimension 2 et 3

Abstract : In 1970, S. Kobayashi asked the question of the hyperbolicity of generic hypersurfaces (and their complement) of high degree in the complex projective space. In the first part of this thesis the hyperbolicity of the complement of generic curves with two components of sufficiently high degrees is proved. In the second part, Demailly's jets are studied in dimension 3 and their algebraic characterization is given. Using the theory of representation of the general linear group, we give the structure of the graded bundle of jets of order 3 in dimension 3, important step to obtain theorems of hyperbolicity. The non existence of global jets of order 2 on smooth hypersurfaces of the projective space of dimension 4 is proved and justifies the necessity to work with jets of order 3.
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https://tel.archives-ouvertes.fr/tel-00007896
Contributor : Erwan Rousseau <>
Submitted on : Monday, January 3, 2005 - 9:54:18 PM
Last modification on : Wednesday, September 16, 2020 - 9:56:26 AM
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Erwan Rousseau. Sur la conjecture de Kobayashi et l'hyperbolicité des hypersurfaces projectives en dimension 2 et 3. Mathématiques [math]. Université de Bretagne occidentale - Brest, 2004. Français. ⟨tel-00007896⟩

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