Comptes Rendus
no. 15-16
Algebraic Geometry/Differential Geometry
Holomorphic Cartan geometries on uniruled surfaces
[Géométries de Cartan holomorphes des surfaces uniréglées]

Présenté par : the Editorial Board

Benjamin McKay1
1 School of Mathematical Sciences, University College Cork, Cork, Ireland
Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 893-896.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.021
Benjamin McKay 1

1 School of Mathematical Sciences, University College Cork, Cork, Ireland 
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Benjamin McKay. Holomorphic Cartan geometries on uniruled surfaces. Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 893-896. doi : 10.1016/j.crma.2011.07.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.021/

[1] Indranil Biswas; Benjamin McKay Holomorphic Cartan geometries and rational curves, May 2010 | arXiv

[2] William M. Goldman Locally homogeneous geometric manifolds (Rajendra Bhatia, ed.), Proceedings of the International Congress of Mathematicians, Hyderabad, vol. 2, Hindawi, 2010, pp. 717-744

[3] Alan T. Huckleberry The classification of homogeneous surfaces, Expo. Math., Volume 4 (1986) no. 4, pp. 289-334

[4] George Daniel Mostow 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] Peter J. Olver Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, 1995 (MR 96i:58005)

[6] Richard W. Sharpe 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)

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