Representation varieties of algebras with nodes

Abstract

We study the behavior of representation varieties of quivers with relations under the operation of node splitting. Working in the "relative setting" (splitting one node at a time) allows us to combinatorially enumerate irreducible components of representation varieties, and show they have rational singularities, for a wide class of algebras. This class contains all radical square zero algebras but also many others, as illustrated by examples throughout the paper. We also give applications to generic decomposition within irreducible components and decomposition of moduli spaces of semistable representations of certain algebras.