Pressland, M orcid.org/0000-0002-9631-3583 and Sauter, J (2022) On Quiver Grassmannians and Orbit Closures for Gen-Finite Modules. Algebras and Representation Theory, 25 (2). pp. 413-445. ISSN 1386-923X
Abstract
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Desingularisation; Quiver Grassmannian; Representation variety; Tilting theory |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Jan 2021 14:36 |
Last Modified: | 25 Jun 2023 22:32 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10468-021-10028-y |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:169552 |
Download
Filename: Pressland-Sauter2022_Article_OnQuiverGrassmanniansAndOrbitC.pdf
Licence: CC-BY 4.0