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Symplectic resolutions for nilpotent orbits. II. (English. Abridged French version) Zbl 1073.14547

Summary: Based on our previous work [Invent. Math. 151, 167–186 (2003; Zbl 1072.14058), see also Part I, C. R., Math., Acad. Sci. Paris 336, No. 2, 159–162 (2003; Zbl 1068.14055)], we prove that, given any two projective symplectic resolutions \(Z_1\) and \(Z_2\) of a nilpotent orbit closure in a complex simple Lie algebra of classical type, \(Z_1\) is deformation equivalent to \(Z_2\). This provides support for a ‘folklore’ conjecture on symplectic resolutions for symplectic singularities.

MSC:

14L30 Group actions on varieties or schemes (quotients)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
17B20 Simple, semisimple, reductive (super)algebras
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References:

[1] Beauville, A., Symplectic singularities, Invent. Math., 139, 541-549 (2000) · Zbl 0958.14001
[2] Collingwood, D.; Mc Govern, W., Nilpotent Orbits in Semi-Simple Lie Algebras (1993), Van Nostrand Reinhold: Van Nostrand Reinhold New York
[3] Fu, B., Symplectic resolutions for nilpotent orbits, Invent. Math., 151, 167-186 (2003) · Zbl 1072.14058
[4] Fu, B.; Namikawa, Y., Uniqueness of crepant resolutions and symplectic singularities · Zbl 1063.14018
[5] Hesselink, W., Polarizations in the classical groups, Math. Z., 160, 217-234 (1978) · Zbl 0364.20048
[6] Huybrechts, D., Compact hyper-Kähler manifolds: basic results, Invent. Math., 135, 63-113 (1999) · Zbl 0953.53031
[7] Kaledin, D., Symplectic resolutions: deformations and birational maps · Zbl 1182.53078
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