On quiver Grassmannians and orbit closures for representation-finite algebras
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- 作者：William Crawley-Boevey ; Julia Sauter
- 关键词：Quiver Grassmannian ; Representation variety ; Auslander algebra ; Tilting theory
- 刊名：Mathematische Zeitschrift
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：285
- 期：1-2
- 页码：367-395
- 全文大小：599KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Springer Berlin Heidelberg
- ISSN：1432-1823
- 卷排序：285
文摘
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.