Decomposing moduli of representations of finite-dimensional algebras

Abstract

Consider a finite-dimensional algebra A and any of its moduli spaces M(A,d)θss of representations. We prove a decomposition theorem which relates any irreducible component of M(A,d)θss to a product of simpler moduli spaces via a finite and birational map. Furthermore, this morphism is an isomorphism when the irreducible component is normal. As an application, we show that the irreducible components of all moduli spaces associated to tame (or even Schur-tame) algebras are rational varieties.