A characterization of nilpotent orbit closures among symplectic singularities

TL;DR

This paper classifies certain conical symplectic varieties with maximal weight 1, showing they are either affine spaces or nilpotent orbit closures, thus clarifying their structure within symplectic singularities.

Contribution

It provides a complete characterization of conical symplectic varieties with maximal weight 1, identifying them explicitly as affine spaces or nilpotent orbit closures.

Findings

Conical symplectic varieties with maximal weight 1 are either affine spaces or nilpotent orbit closures.

The classification links symplectic singularities to well-understood geometric objects.

The result simplifies understanding of symplectic singularities with specific weight conditions.

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.