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.
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.
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@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 = {https://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 - https://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 -
Fu, Baohua. Symplectic resolutions for nilpotent orbits (III). Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 585-588. doi : 10.1016/j.crma.2006.02.004. https://www.numdam.org/articles/10.1016/j.crma.2006.02.004/
[1] Symplectic singularities, Invent. Math., Volume 139 (2000), pp. 541-549
[2] 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] 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] Symplectic resolutions for nilpotent orbits, Invent. Math., Volume 151 (2003), pp. 167-186
[5] Mukai flops and deformations of symplectic resolutions (Math. Z., in press) | arXiv
[6] Polarization in the classical groups, Math. Z., Volume 160 (1978), pp. 217-234
[7] HyperKähler manifolds and birational transformations, Adv. Theor. Math. Phys., Volume 6 (2002) no. 3, pp. 557-574
[8] Birational geometry of symplectic resolutions of nilpotent orbits | arXiv
[9] Small contractions of symplectic 4-folds, Duke Math. J., Volume 120 (2003) no. 1, pp. 65-95
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