Uniqueness of crepant resolutions and symplectic singularities
[Unicité des résolutions crépantes et singularités symplectiques]
Fu, Baohua1 ; Namikawa, Yoshinori2
1 Université de Nice, Parc Valrose, Laboratoire J.A. Dieudonné, 06108 Nice cedex 02 (France)
2 Departement of Mathematics, Kyoto University, Graduate School of Science, Kiat-Shirakawa Oiwake-cho, Kyoto 606-8502 (Japon)
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 1-19.

Nous démontrons l'unicité des résolutions crépantes pour certaines singularités quotient et pour certaines adhérences d'orbites nilpotentes. La finitude des résolutions symplectiques non-isomorphes pour les singularités symplectiques de dimension 4 est démontrée. Nous construisons aussi un exemple d'une singularité symplectique qui admet deux résolutions symplectiques non-équivalentes.

We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4- dimensional symplectic singularities is proved. We also give an example of a symplectic singularity which admits two non-equivalent symplectic resolutions.

DOI : 10.5802/aif.2008
Classification : 14E15
Keywords: crepant resolutions, symplectic singularities
Mot clés : résolutions crépantes, singularités symplectiques
Fu, Baohua 1 ; Namikawa, Yoshinori 2

1 Université de Nice, Parc Valrose, Laboratoire J.A. Dieudonné, 06108 Nice cedex 02 (France)
2 Departement of Mathematics, Kyoto University, Graduate School of Science, Kiat-Shirakawa Oiwake-cho, Kyoto 606-8502 (Japon) 
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Fu, Baohua; Namikawa, Yoshinori. Uniqueness of crepant resolutions and symplectic singularities. Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 1-19. doi : 10.5802/aif.2008. http://www.numdam.org/articles/10.5802/aif.2008/

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