On quiver Grassmannians and orbit closures for gen-finite modules

Pressland, Matthew; Sauter, Julia

doi:10.1007/s10468-021-10028-y

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On quiver Grassmannians and orbit closures for gen-finite modules

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Pressland, Matthew
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10468-021-10028-y
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https://doi.org/10.48550/arXiv.1802.01848
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Pressland-Sauter_On quiver Grassmannians and orbit closures for gen-finite modules_2022.pdf
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Citation

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

Cite as: https://hdl.handle.net/21.11116/0000-000A-A692-5

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.