Comptes Rendus
no. 2
Algebraic Geometry
Symplectic resolutions for coverings of nilpotent orbits

Presented by: Jean-Pierre Demailly

Baohua Fu1
1 Laboratoire J.A.Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 2, France
Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 159-162.

Let 𝒪 be a nilpotent orbit in a semisimple complex Lie algebra 𝔤. Denote by G the simply connected Lie group with Lie algebra 𝔤. For a G-homogeneous covering M→𝒪, let X be the normalization of 𝒪 ¯ in the function field of M. In this Note, we study the existence of symplectic resolutions for such coverings X.

Soit 𝒪 une orbite nilpotente dans une algèbre de Lie semi-simple complexe 𝔤. Soit G le groupe de Lie simplement connexe d'algèbre de Lie 𝔤. Pour un revêtement G-homogène M→𝒪, notons X la normalisation de 𝒪 ¯ dans le corps de fonctions de M. Dans cette Note, nous étudions les résolutions symplectiques pour de telles variétés X.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00011-6

Baohua Fu 1

1 Laboratoire J.A.Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 2, France 
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Baohua Fu. Symplectic resolutions for coverings of nilpotent orbits. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 159-162. doi : 10.1016/S1631-073X(03)00011-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00011-6/

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[2] D. Collingwood; W. Mc Govern Nilpotent Orbits in Semi-Simple Lie Algebras, Van Nostrand–Reinhold, New York, 1993

[3] B. Fu Symplectic resolutions for nilpotent orbits, Invent. Math., Volume 151 (2003), pp. 167-186

[4] W. Hesselink Polarizations in the classical groups, Math. Z., Volume 160 (1978), pp. 217-234

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