Decomposing moduli of representations of finite-dimensional algebras

Abstract

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d}{)}_{\theta }^{ss}$ of representations. We prove a decomposition theorem which relates any irreducible component of $\mathcal{M}(A,\mathbf{d}{)}_{\theta }^{ss}$ 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 example application, we show that the irreducible components of all moduli spaces associated to tame (or even Schur-tame) algebras are rational varieties.

23 pages. v2: various minor improvements, final published version

References in corpus (4)

• A functorial construction of moduli of sheaves
• The geometry of finite dimensional algebras with vanishing radical square
• Moduli spaces of representations of special biserial algebras
• On moduli spaces for quasi-tilted algebras

Cited by in corpus (2)

• Algorithms for representations of quiver Yangian algebras
• Representation varieties of algebras with nodes