Singular Quiver Varieties over Extended Dynkin Quivers

TL;DR

This paper classifies singularities in certain Nakajima quiver varieties related to extended Dynkin quivers and constructs hyper-Kähler cobordisms between binary polyhedral spaces, advancing understanding of their geometric structures.

Contribution

It provides a classification of singularities in unframed Nakajima quiver varieties for extended Dynkin quivers and constructs hyper-Kähler cobordisms, revealing new geometric relationships.

Findings

Classification of singularities in specific quiver varieties

Construction of hyper-Kähler cobordisms between binary polyhedral spaces

Insights into the geometric structure of extended Dynkin quiver varieties

Abstract

We classify the singularities in the unframed Nakajima quiver varieties associated with extended Dynkin quivers and the corresponding minimal imaginary root with a small restriction on the parameter and use this to construct a number of hyper-K\"{a}hler cobordisms between binary polyhedral spaces.