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  On quiver Grassmannians and orbit closures for gen-finite modules

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000A-A692-5 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-1C58-1
Genre: Journal Article

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 Creators:
Pressland, Matthew1, Author           
Sauter, Julia, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Rings and Algebras, Algebraic Geometry, Representation Theory
 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.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 1802.01848
DOI: 10.1007/s10468-021-10028-y
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Title: Algebras and Representation Theory
  Abbreviation : Algebr. Represent. Theory
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 25 (2) Sequence Number: - Start / End Page: 413 - 445 Identifier: -