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On Quiver Grassmannians and Orbit Closures for Gen-Finite Modules
Algebras and Representation Theory ( IF 0.6 ) Pub Date : 2021-05-27 , DOI: 10.1007/s10468-021-10028-y
Matthew Pressland , Julia Sauter

We show that endomorphism rings of cogenerators in the module category of a finite-dimensional algebra A admit a canonical tilting module, whose tilted algebra B is related to A by a recollement. Let M be a gen-finite A-module, meaning there are only finitely many indecomposable modules generated by M. Using the canonical tilts of endomorphism algebras of suitable cogenerators associated to M, and the resulting recollements, we construct desingularisations of the orbit closure and quiver Grassmannians of M, thus generalising all results from previous work of Crawley-Boevey and the second author in 2017. We provide dual versions of the key results, in order to also treat cogen-finite modules.



中文翻译:

关于 Gen-Finite 模块的 Quiver Grassmannians 和轨道闭合

我们证明了有限维代数A的模范畴中热电偶的自同态环承认一个规范倾斜模,其倾斜代数BA相关联。令M是一个生成有限A 模,这意味着M生成的不可分解模只有有限多个。使用与M相关联的合适热电联发生器的自同态代数的规范倾斜,以及由此产生的回忆,我们构建了M的轨道闭合和颤抖格拉斯曼数的去奇异化,从而概括了 Crawley-Boevey 和第二作者在 2017 年之前工作的所有结果。我们提供了关键结果的双重版本,以便也处理同构有限模块。

更新日期:2021-05-28
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