On the structure of homogeneous symplectic varieties of complete intersection

TL;DR

This paper proves that homogeneous symplectic varieties that are complete intersections in affine space are precisely the nilpotent varieties associated with semisimple Lie algebras.

Contribution

It establishes a classification linking homogeneous symplectic complete intersection varieties to nilpotent varieties of semisimple Lie algebras.

Findings

Homogeneous symplectic complete intersections are nilpotent varieties.

The structure of such varieties is characterized by semisimple Lie algebra theory.

The result provides a classification of these symplectic varieties.

Abstract

If X is a symplectic variety emedded in an affine space as a complete intersection of homogeneous polynomials, then X coincides with the nilpotent variety of a semisimple Lie algebra.