Framed moduli and Grassmannians of submodules

TL;DR

This paper generalizes Reineke's Grassmannian construction for moduli spaces of framed quiver representations to broader algebraic contexts, providing explicit fiber realizations for certain quiver moduli spaces.

Contribution

It extends the Grassmannian realization of moduli spaces to finite dimensional algebras and cyclic quivers, offering new explicit descriptions of moduli space fibers.

Findings

Generalized Reineke's construction to broader algebraic settings

Explicit realization of fibers for specific quiver moduli spaces

Enhanced understanding of moduli space structures

Abstract

In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Marcus Reineke. Obtained is a generalization of this construction for finite dimensional associative algebras and for quivers with oriented cycles. As an application we get an explicit realization of fibers for the moduli space bundle over the categorical quotient for the quiver $A_{n-1}^{(1)}$.