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.
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.
Keywords: 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://www.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://www.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://www.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, Volume 56 (2006) no. 2, pp. 397-421. doi : 10.5802/aif.2187. http://www.numdam.org/articles/10.5802/aif.2187/
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