A characterization of nilpotent orbit closures among symplectic singularities

Abstract

We prove that a conical symplectic variety with maximal weight 1 is isomorphic to one of the following: (i) an affine space with the standard symplectic form (ii) a nilpotent orbit closure of a complex semisimple Lie algebra with the Kirillov-Kostant form.

Version 5: 7 pages, several parts are improved in exposition

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