no. 8
Algebraic Geometry
Symplectic resolutions for nilpotent orbits (III)
[Résolutions symplectiques pour les orbites nilpotentes (III)]

Présenté par : Gérard Laumon

Fu, Baohua1
1 Laboratoire J. Leray (mathématiques), faculté des sciences, 2, rue de la Houssinière, BP 92208, 44322 Nantes cedex 03, France
Comptes Rendus. Mathématique, Tome 342 (2006) no. 8, pp. 585-588.

Nous montrons que deux résolutions symplectiques d'une adhérence d'orbite nilpotente dans une algèbre de Lie simple complexe classique sont réliées l'une à l'autre par des flops de Mukai en codimension 2.

We prove that two symplectic resolutions of a nilpotent orbit closures in a simple complex Lie algebra of classical type are related by Mukai flops in codimension 2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.02.004
Fu, Baohua 1

1 Laboratoire J. Leray (mathématiques), faculté des sciences, 2, rue de la Houssinière, BP 92208, 44322 Nantes cedex 03, France 
@article{CRMATH_2006__342_8_585_0,
     author = {Fu, Baohua},
     title = {Symplectic resolutions for nilpotent orbits {(III)}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {585--588},
     publisher = {Elsevier},
     volume = {342},
     number = {8},
     year = {2006},
     doi = {10.1016/j.crma.2006.02.004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2006.02.004/}
}
TY  - JOUR
AU  - Fu, Baohua
TI  - Symplectic resolutions for nilpotent orbits (III)
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 585
EP  - 588
VL  - 342
IS  - 8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2006.02.004/
DO  - 10.1016/j.crma.2006.02.004
LA  - en
ID  - CRMATH_2006__342_8_585_0
ER  - 
%0 Journal Article
%A Fu, Baohua
%T Symplectic resolutions for nilpotent orbits (III)
%J Comptes Rendus. Mathématique
%D 2006
%P 585-588
%V 342
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2006.02.004/
%R 10.1016/j.crma.2006.02.004
%G en
%F CRMATH_2006__342_8_585_0
Fu, Baohua. Symplectic resolutions for nilpotent orbits (III). Comptes Rendus. Mathématique, Tome 342 (2006) no. 8, pp. 585-588. doi : 10.1016/j.crma.2006.02.004. http://www.numdam.org/articles/10.1016/j.crma.2006.02.004/

[1] Beauville, A. Symplectic singularities, Invent. Math., Volume 139 (2000), pp. 541-549

[2] Burns, D.; Hu, Y.; Luo, T. HyperKähler manifolds and birational transformations in dimension 4, Vector Bundles and Representation Theory, Columbia, MO, 2002, Contemp. Math., vol. 322, Amer. Math. Soc., Providence, RI, 2003, pp. 141-149

[3] Cho, K.; Miyaoka, Y.; Shepherd-Barron, N.I. Characterizations of projective space and applications to complex symplectic manifolds, Higher Dimensional Birational Geometry, Kyoto, 1997, Adv. Stud. Pure Math., vol. 35, Math. Soc. Japan, Tokyo, 2002, pp. 1-88

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

[5] Fu, B. Mukai flops and deformations of symplectic resolutions (Math. Z., in press) | arXiv

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

[7] Hu, Y.; Yau, S.-T. HyperKähler manifolds and birational transformations, Adv. Theor. Math. Phys., Volume 6 (2002) no. 3, pp. 557-574

[8] Namikawa, Y. Birational geometry of symplectic resolutions of nilpotent orbits | arXiv

[9] Wierzba, J.; Wiśniewski, J. Small contractions of symplectic 4-folds, Duke Math. J., Volume 120 (2003) no. 1, pp. 65-95

Cité par Sources :