Steady K\"ahler-Ricci solitons on crepant resolutions of finite quotients of $\mathbb{C}^n$

TL;DR

This paper establishes the existence of steady K"ahler-Ricci solitons on specific geometric resolutions of quotient spaces formed by finite subgroups of SU(n), advancing understanding in complex differential geometry.

Contribution

It proves the existence of steady K"ahler-Ricci solitons on equivariant crepant resolutions of quotient spaces of complex Euclidean space by finite subgroups of SU(n).

Findings

Existence of steady K"ahler-Ricci solitons on crepant resolutions.

Construction of such solitons in the equivariant setting.

Extension of Ricci soliton theory to quotient singularities.

Abstract

We prove the existence of steady K\"ahler-Ricci solitons on equivariant crepant resolutions of $\mathbb{C}^n/G$, where $G$ is a finite subgroup of $SU(n)$.