Decomposing moduli of representations of finite-dimensional algebras. (English) Zbl 1434.16006
Summary: Consider a finite-dimensional algebra \(A\) and any of its moduli spaces \(\mathcal{M}(A,\mathbf{d})^{ss}_\theta\) of representations. We prove a decomposition theorem which relates any irreducible component of \(\mathcal{M}(A,\mathbf{d})^{ss}_\theta\) 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.
MSC:
| 16G20 | Representations of quivers and partially ordered sets |
| 14L24 | Geometric invariant theory |
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
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