Decomposing moduli of representations of finite-dimensional algebras

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Abstract

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.

Mathematics Subject Classification

16G20 14L24 14D20 

Notes

Acknowledgements

We wish to thank Grzegorz Bobiński and Alastair King for discussions that led to improvements of our paper. We are especially thankful to Harm Derksen for clarifying discussions on some of the results in [35]. The first author (C.C.) was supported by the NSA under grant H98230-15-1-0022.

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Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Missouri-ColumbiaMOUSA
  2. 2.Department of MathematicsUniversity of IowaIowa CityUSA

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