Comptes Rendus
no. 15-16
Algebraic Geometry/Differential Geometry
Holomorphic Cartan geometries on uniruled surfaces

Presented by: 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.

We classify holomorphic Cartan geometries on every compact complex surface which contains a rational curve.

Dans cette Note nous classifions les géométries de Cartan holomorphes sur toute surface complexe compacte contenant une courbe rationnelle.

Received:
Accepted:
Published online:
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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