Desingularizations of quiver Grassmannians via graded quiver varieties

TL;DR

This paper extends desingularization techniques for quiver Grassmannians to broader classes, utilizing Nakajima's graded quiver varieties, and applies to modules over iterated tilted algebras of Dynkin type.

Contribution

It generalizes desingularizations of quiver Grassmannians beyond Dynkin quivers using Nakajima's framework, covering iterated tilted algebras.

Findings

Desingularization maps constructed for broader classes of quiver Grassmannians.

Application to modules over iterated tilted algebras of Dynkin type.

Extension of previous desingularization methods.

Abstract

Inspired by recent work of Cerulli-Feigin-Reineke on desingularizations of quiver Grassmannians of representations of Dynkin quivers, we obtain desingularizations in considerably more general situations and in particular for Grassmannians of modules over iterated tilted algebras of Dynkin type. Our desingularization map is constructed from Nakajima's desingularization map for graded quiver varieties.