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.
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.
Keywords: crepant resolutions, symplectic singularities
Mot clés : résolutions crépantes, singularités symplectiques
@article{AIF_2004__54_1_1_0, author = {Fu, Baohua and Namikawa, Yoshinori}, title = {Uniqueness of crepant resolutions and symplectic singularities}, journal = {Annales de l'Institut Fourier}, pages = {1--19}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {1}, year = {2004}, doi = {10.5802/aif.2008}, mrnumber = {2069119}, zbl = {1063.14018}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2008/} }
TY - JOUR AU - Fu, Baohua AU - Namikawa, Yoshinori TI - Uniqueness of crepant resolutions and symplectic singularities JO - Annales de l'Institut Fourier PY - 2004 SP - 1 EP - 19 VL - 54 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2008/ DO - 10.5802/aif.2008 LA - en ID - AIF_2004__54_1_1_0 ER -
%0 Journal Article %A Fu, Baohua %A Namikawa, Yoshinori %T Uniqueness of crepant resolutions and symplectic singularities %J Annales de l'Institut Fourier %D 2004 %P 1-19 %V 54 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2008/ %R 10.5802/aif.2008 %G en %F AIF_2004__54_1_1_0
Fu, Baohua; Namikawa, Yoshinori. Uniqueness of crepant resolutions and symplectic singularities. Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 1-19. doi : 10.5802/aif.2008. http://archive.numdam.org/articles/10.5802/aif.2008/
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