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)

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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.
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
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

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