Crepant resolutions of a Slodowy slice in a nilpotent orbit closure in $\mathfrak{sl}_N(\mathbb{C})$

TL;DR

This paper investigates crepant resolutions of Slodowy slices within nilpotent orbit closures in rak{sl}_N(\u00a3), showing they derive from resolutions of the orbit closure and providing a method to count them.

Contribution

It demonstrates that all crepant resolutions of a Slodowy slice are restrictions of those of the orbit closure and introduces a decomposition technique for counting resolutions.

Findings

Every crepant resolution of a Slodowy slice is a restriction of a resolution of the orbit closure.

A decomposition of the Slodowy slice allows for counting crepant resolutions.

The paper establishes structural properties of Slodowy slices in rak{sl}_N(\u00a3).

Abstract

One of our results of this article is that every (projective) crepant resolution of a Slodowy slice in a nilpotent orbit closure in $\mathfrak{sl}_N(\mathbb{C})$ can be obtained as the restriction of some crepant resolution of the nilpotent orbit closure. We also show that there is a decomposition of the Slodowy slice into other Slodowy slices with good properties. From this decomposition, one can count the number of crepant resolutions.