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Derived equivalences of selfinjective algebras preserve singularities

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Abstract.

We prove that the derived equivalences (more generally the stable equivalences of Morita type) of finite dimensional selfinjective algebras over algebraically closed fields preserve the types of singularities in the orbit closures of module varieties. As an application, we obtain that the orbit closures in the module varieties of the Brauer tree algebras are normal and Cohen-Macaulay.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

    Andrzej Skowroński & Grzegorz Zwara

Authors
  1. Andrzej Skowroński
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  2. Grzegorz Zwara
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Correspondence to Andrzej Skowroński.

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Mathematics Subject Classification (2000): 14B05, 14L30, 16D50, 16G20

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Skowroński, A., Zwara, G. Derived equivalences of selfinjective algebras preserve singularities. manuscripta math. 112, 221–230 (2003). https://doi.org/10.1007/s00229-003-0396-y

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  • DOI: https://doi.org/10.1007/s00229-003-0396-y

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