On quiver Grassmannians and orbit closures for representation-finite algebras

We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective–injective; its endomorphism ring is called the projective quotient algebra. For any representation-finite algebra, we use the projective quotient algebra to construct desingu...

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Veröffentlicht in:Mathematische Zeitschrift 2017-02, Vol.285 (1-2), p.367-395
Hauptverfasser: Crawley-Boevey, William, Sauter, Julia
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective–injective; its endomorphism ring is called the projective quotient algebra. For any representation-finite algebra, we use the projective quotient algebra to construct desingularizations of quiver Grassmannians, orbit closures in representation varieties, and their desingularizations. This generalizes results of Cerulli Irelli, Feigin and Reineke.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-016-1712-z