Sur la conjecture de remmert

Bertrand Deroin

Sur la conjecture de remmert

Bertrand Deroin

CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

This paper is a survey of the main works on the so-called Remmert's conjecture, if Xⁿ is a closed, homogeneous complex manifold with automorphism group Aut(X) then dim(Aut(X) ≤ n² + 2n. We describe the structure of a closed, homogeneous complex manifold X, prove Remmert's conjecture for Kähler homogeneous manifolds, then describe the counterexamples constructed by Snow and Winkelman with dim(X) = 3m + 1 and dim(Aut(X) = 3^m + 3m, and finally show Akhiezer's theorem (which gives a bound on dim(Au(X)) for fixed n, being thus a weak version of Remmert's conjecture).

langue originale	Français
Pages (de - à)	213-234
Nombre de pages	22
journal	Boletin de la Sociedad Matematica Mexicana
Volume	9
Numéro de publication	2
état	Publié - 1 janv. 2003
Modification externe	Oui

mots-clés

Automorphism group acting on complex manifold
Complex Lie group
Homogeneous complex manifold

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Contient cette citation

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AB - This paper is a survey of the main works on the so-called Remmert's conjecture, if Xn is a closed, homogeneous complex manifold with automorphism group Aut(X) then dim(Aut(X) ≤ n2 + 2n. We describe the structure of a closed, homogeneous complex manifold X, prove Remmert's conjecture for Kähler homogeneous manifolds, then describe the counterexamples constructed by Snow and Winkelman with dim(X) = 3m + 1 and dim(Aut(X) = 3m + 3m, and finally show Akhiezer's theorem (which gives a bound on dim(Au(X)) for fixed n, being thus a weak version of Remmert's conjecture).

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