Dans cet article nous faisons l’étude algébrique des jets de Demailly-Semple en dimension 3 en utilisant la théorie des invariants des groupes non réductifs. Cette étude fournit la caractérisation géométrique du fibré des jets d’ordre 3 sur une variété de dimension 3 et permet d’effectuer, par Riemann-Roch, un calcul de caractéristique d’Euler.
In this article, the algebraic characterization of Demailly-Semple jets in dimension 3 is given using the invariant theory of non reductive groups. This work provides the geometric characterization of the 3-jets bundle on a manifold of dimension 3 and, by Riemann-Roch, the computation of the Euler characteristic.
Mots-clés : hyperbolicité des variétés complexes, huperbolicité au sens de Kobayashi, fibrés des jets de différentielles, représentations des groupes linéaires, théorie des invariants des groupes non réductifs
@article{AIF_2006__56_2_397_0, author = {Rousseau, Erwan}, title = {\'Etude des jets de {Demailly-Semple} en dimension 3}, journal = {Annales de l'Institut Fourier}, pages = {397--421}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {56}, number = {2}, year = {2006}, doi = {10.5802/aif.2187}, zbl = {1092.58003}, mrnumber = {2226021}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2187/} }
TY - JOUR AU - Rousseau, Erwan TI - Étude des jets de Demailly-Semple en dimension 3 JO - Annales de l'Institut Fourier PY - 2006 SP - 397 EP - 421 VL - 56 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2187/ DO - 10.5802/aif.2187 LA - fr ID - AIF_2006__56_2_397_0 ER -
%0 Journal Article %A Rousseau, Erwan %T Étude des jets de Demailly-Semple en dimension 3 %J Annales de l'Institut Fourier %D 2006 %P 397-421 %V 56 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2187/ %R 10.5802/aif.2187 %G fr %F AIF_2006__56_2_397_0
Rousseau, Erwan. Étude des jets de Demailly-Semple en dimension 3. Annales de l'Institut Fourier, Tome 56 (2006) no. 2, pp. 397-421. doi : 10.5802/aif.2187. http://archive.numdam.org/articles/10.5802/aif.2187/
[1] Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials, Proc. Sympos. Pure Math., Volume 62, Amer. Math.Soc., Providence, RI (1997), pp. 285-360 | MR | Zbl
[2] Hyperbolicity of generic surfaces of high degree in projective 3-space, Amer. J. Math, Volume 122 (2000), pp. 515-546 | DOI | MR | Zbl
[3] Logarithmic jet bundles and applications, Osaka J. of Math., Volume 38 (2001), pp. 185-237 | MR | Zbl
[4] Hyperbolicity of the complement of plane algebraic curves, Amer.J. Math, Volume 117 (1995), pp. 573-599 | DOI | MR | Zbl
[5] On the hyperbolicity of the complements of curves in algebraic surfaces : the three component case, Duke. Math. J., Volume 78 (1995), pp. 193-212 | DOI | MR | Zbl
[6] Young Tableaux, London Mathematical Society Student Texts 35, Cambrige University Press, 1997 | MR | Zbl
[7] Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979, Proc. Inter. Sympos. Berkeley, CA, Springer-Verlag, New-York (1980), pp. 41-74 | MR | Zbl
[8] On the logarithmic Kodaira dimension of algebraic varieties, Complex Anal. and Alg. Geom., Ianami Shoten (1977), pp. 175-189 | MR | Zbl
[9] Geometry on complements of lines in , Tokyo J. Math., Volume 1 (1978), pp. 1-19 | DOI | MR | Zbl
[10] On complex manifolds with positive tangent bundles, Journal of the Mathematical Society of Japan, Volume 22 (1970), pp. 499-525 | DOI | MR | Zbl
[11] Invariant theory, LNM, Volume 1278 (1987)
[12] Invariant theory, 4, EMS, Springer-Verlag, 1989
[13] Classical invariant theory, Brandeis Lect. Notes, Volume 1 (1982) | MR
[14] Sur la conjecture de Kobayashi et l’hyperbolicité des hypersurfaces projectives en dimension 2 et 3 (Université de Bretagne Occidentale)
[15] Hyperbolicité du complémentaire d’une courbe : le cas de deux composantes, CRAS, Volume Ser. I 336 (2003), pp. 635-640 | MR | Zbl
[16] Symmetric powers of the cotangent bundle and classification of algebraic varieties, Lect. Notes in Math., Volume 732, Berlin, Heidelberg, New York, Springer (1979) | MR | Zbl
[17] Hyperbolicity of the complement of a generic smooth curve of high degree in the complex projective plane, Invent. Math., Volume 124 (1996), pp. 573-618 | DOI | MR | Zbl
[18] On the Popov-Pommerening conjecture for groups of type , Proc. AMS, Volume 106 (1989), pp. 611-616 | MR | Zbl
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