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Decomposing moduli of representations of finite-dimensional algebras

Authors
  • Chindris, Calin1
  • Kinser, Ryan2
  • 1 University of Missouri-Columbia, Mathematics Department, MO, Columbia, USA , MO (United States)
  • 2 University of Iowa, Department of Mathematics, Iowa City, IA, USA , Iowa City (United States)
Type
Published Article
Journal
Mathematische Annalen
Publisher
Springer Berlin Heidelberg
Publication Date
May 16, 2018
Volume
372
Issue
1-2
Pages
555–580
Identifiers
DOI: 10.1007/s00208-018-1687-7
Source
Springer Nature
Keywords
License
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Abstract

Consider a finite-dimensional algebra A and any of its moduli spaces M(A,d)θss\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {M}}}(A,\mathbf {d})^{ss}_{\theta }$$\end{document} of representations. We prove a decomposition theorem which relates any irreducible component of M(A,d)θss\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {M}}}(A,{\mathbf {d}})^{ss}_{\theta }$$\end{document} 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.

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