Proof of the Ginzburg-Kazhdan conjecture

TL;DR

This paper proves a conjecture by Ginzburg and Kazhdan that the affine closure of the cotangent bundle of a basic affine space has specific symplectic singularities, is $ ext{Q}$-factorial, and has terminal singularities.

Contribution

It confirms the Ginzburg-Kazhdan conjecture by establishing the nature of singularities in the affine closure of the cotangent bundle of a basic affine space.

Findings

Affine closure has conical symplectic singularities

The variety is $ ext{Q}$-factorial

The variety has terminal singularities

Abstract

We prove that the affine closure of the cotangent bundle of the basic affine space of a complex semisimple group has conical symplectic singularities, which confirms a conjecture of Ginzburg and Kazhdan. We also show that this variety is $\mathbb{Q}$-factorial and has terminal singularities.