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In this paper, firstly we calculate Picard groups of a nilpotent orbit O in a classical complex simple Lie algebra and discuss the properties of being Q-factorial and factorial for the normalization Õ of the closure of O. Then we consider the problem of symplectic resolutions for Õ. Our main theorem says that for any nilpotent orbit O in a semi-simple(More)
Based on our previous work [3], we prove that for any two projective symplectic resolutions Z1 and Z2 for a nilpotent orbit closure in a simple complex Lie algebra of classical type, then Z1 is deformation equivalent to Z2. This provides support for a “folklore” conjecture on symplectic resolutions for symplectic singularities.
Let X be a smooth irreducible complex variety and G a finite subgroup of Aut(X). There is a natural action of G on T ∗X preserving the canonical symplectic form. We show that if T ∗X/G admits a symplectic resolution π : Z → T ∗X/G, then X/G is smooth and Z contains an open set isomorphic to T ∗(X/G). In the case of X = P and G ⊂ SL(n + 1,C), we give an(More)