On quiver Grassmannians and orbit closures for gen-finite modules
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916632107941888 |
|---|---|
| author | Pressland, Matthew Sauter, Julia |
| author_facet | Pressland, Matthew Sauter, Julia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_01848 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On quiver Grassmannians and orbit closures for gen-finite modules Pressland, Matthew Sauter, Julia Rings and Algebras Algebraic Geometry Representation Theory 16G10 (Primary), 14L30, 14M15 (Secondary) 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. |
| title | On quiver Grassmannians and orbit closures for gen-finite modules |
| topic | Rings and Algebras Algebraic Geometry Representation Theory 16G10 (Primary), 14L30, 14M15 (Secondary) |
| url | https://arxiv.org/abs/1802.01848 |