On quiver Grassmannians and orbit closures for gen-finite modules

Pressland, M. and Sauter, J. (2022) On quiver Grassmannians and orbit closures for gen-finite modules. Algebras and Representation Theory, 25(2), pp. 413-445. (doi: 10.1007/s10468-021-10028-y)

Abstract

We show that endomorphism rings of cogenerators in the module category of a finite-dimensional algebra A admit a canonical tilting module. The tilted algebra B is related to A by a recollement. We call an A-module M gen-finite if 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 with A, 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.

• Item Type: Articles
• Additional Information: Open Access funding enabled and organized by Projekt DEAL.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pressland, Dr Matthew
• Authors: Pressland, M., and Sauter, J.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Algebras and Representation Theory
• Publisher: Springer
• ISSN: 1386-923X
• ISSN (Online): 1572-9079
• Published Online: 27 May 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in Algebras and Representation Theory 25(2): 413-445
• Publisher Policy: Reproduced under a Creative Commons License