Lehmann, Ralf
Complex-symmetric spaces
Annales de l'institut Fourier, Tome 39 (1989) no. 2 , p. 373-416
Zbl 0649.32021 | MR 91d:32048
doi : 10.5802/aif.1171
URL stable : http://www.numdam.org/item?id=AIF_1989__39_2_373_0

Un espace compact complexe X est appelé complexe-symétrique relatif à un sous-groupe G du groupe Aut θ (X) si chaque point xX est un point fixe isolé d’un automorphisme involutif dans G. Il en résulte que X est presque G 0 -homogène. Après quelques exemples nous classifions les variétés complexes-symétriques normales avec G 0 réductif. Nous prouvons que X est un produit d’un espace hermitien symétrique et d’un plongement d’un tore algébrique satisfaisant quelques conditions supplémentaires. Dans le cas lisse ces plongements sont classifiés en utilisant la description d’un plongement par un système de cônes (éventails) et la théorie de groupes de Coxeter.
A compact complex space X is called complex-symmetric with respect to a subgroup G of the group Aut 0 (X), if each point of X is isolated fixed point of an involutive automorphism of G. It follows that G is almost G 0 -homogeneous. After some examples we classify normal complex-symmetric varieties with G 0 reductive. It turns out that X is a product of a Hermitian symmetric space and a compact torus embedding satisfying some additional conditions. In the smooth case these torus embeddings are classified using the description of torus embeddings by systems of cone (“fans”) and the theory of Coxeter groups.

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