On the structure of homogeneous symplectic varieties of complete intersection

Details On the structure of homogeneous symplectic varieties of complete intersection On the structure of homogeneous symplectic varieties of complete intersection

2012-01-26

arxiv.org/abs/1201.5444v2

Mathematics

Algebraic Geometry

16 pages (version 2: New remarks are added.)

Scientific paper

If X is a symplectic variety emedded in an affine space as a complete intersection of homogeneous polynomials, then X coincides with a nilpotent orbit closure of a semisimple Lie algebra. Moreover, if X is a homogeneous symplectic hypersurface, then dim X = 2 and X is an A_1-surface singularity. In the final remark we introduce another proof of Fu's theorem on the crepant resolution of a nilpotent orbit closure, which can be regarded as a translation of the original proof into contact geometry.

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