Dans cette Note nous classifions les géométries de Cartan holomorphes sur toute surface complexe compacte contenant une courbe rationnelle.
We classify holomorphic Cartan geometries on every compact complex surface which contains a rational curve.
Accepté le :
Publié le :
@article{CRMATH_2011__349_15-16_893_0, author = {McKay, Benjamin}, title = {Holomorphic {Cartan} geometries on uniruled surfaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {893--896}, publisher = {Elsevier}, volume = {349}, number = {15-16}, year = {2011}, doi = {10.1016/j.crma.2011.07.021}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2011.07.021/} }
TY - JOUR AU - McKay, Benjamin TI - Holomorphic Cartan geometries on uniruled surfaces JO - Comptes Rendus. Mathématique PY - 2011 SP - 893 EP - 896 VL - 349 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.07.021/ DO - 10.1016/j.crma.2011.07.021 LA - en ID - CRMATH_2011__349_15-16_893_0 ER -
%0 Journal Article %A McKay, Benjamin %T Holomorphic Cartan geometries on uniruled surfaces %J Comptes Rendus. Mathématique %D 2011 %P 893-896 %V 349 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.07.021/ %R 10.1016/j.crma.2011.07.021 %G en %F CRMATH_2011__349_15-16_893_0
McKay, Benjamin. Holomorphic Cartan geometries on uniruled surfaces. Comptes Rendus. Mathématique, Tome 349 (2011) no. 15-16, pp. 893-896. doi : 10.1016/j.crma.2011.07.021. http://www.numdam.org/articles/10.1016/j.crma.2011.07.021/
[1] Holomorphic Cartan geometries and rational curves, May 2010 | arXiv
[2] Locally homogeneous geometric manifolds (Bhatia, Rajendra, ed.), Proceedings of the International Congress of Mathematicians, Hyderabad, vol. 2, Hindawi, 2010, pp. 717-744
[3] The classification of homogeneous surfaces, Expo. Math., Volume 4 (1986) no. 4, pp. 289-334
[4] The extensibility of local Lie groups of transformations and groups on surfaces, Ann. of Math. (2), Volume 52 (1950), pp. 606-636 MR 0048464 (14,18d)
[5] Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, 1995 (MR 96i:58005)
[6] Differential Geometry, Graduate Texts in Mathematics, vol. 166, Springer-Verlag, New York, 1997 (Cartanʼs generalization of Kleinʼs Erlangen program, with a foreword by S.S. Chern), MR MR1453120 (98m:53033)
Cité par Sources :