Simple tilts of length hearts and simple-minded mutation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917737045950464 |
|---|---|
| author | Broomhead, Nathan Simoes, Raquel Coelho Pauksztello, David Woolf, Jon |
| author_facet | Broomhead, Nathan Simoes, Raquel Coelho Pauksztello, David Woolf, Jon |
| contents | We characterise when a simple Happel-Reiten-Smalo tilt of a length heart is again a length heart in terms of approximation theory and the existence of a stability condition with a phase gap. We apply simple-minded reduction to provide a sufficient condition for infinite iterability of simple-minded mutation/simple tilting. We use simple-minded mutation pairs to provide a common framework to show that mutation of simple-minded collections (resp. $w$-simple-minded systems, for $w \geq 1$) gives simple-minded collections (resp. $w$-simple-minded systems) under mild conditions, in the process providing a unified proof of results of A. Dugas and P. Jorgensen. Finally, we show that under mild conditions, mutation of simple-minded collections is compatible with mutation of $w$-simple-minded systems via a singularity category construction due to H. Jin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple tilts of length hearts and simple-minded mutation Broomhead, Nathan Simoes, Raquel Coelho Pauksztello, David Woolf, Jon Representation Theory Algebraic Geometry Category Theory 18G80, 14F08, 16E35 We characterise when a simple Happel-Reiten-Smalo tilt of a length heart is again a length heart in terms of approximation theory and the existence of a stability condition with a phase gap. We apply simple-minded reduction to provide a sufficient condition for infinite iterability of simple-minded mutation/simple tilting. We use simple-minded mutation pairs to provide a common framework to show that mutation of simple-minded collections (resp. $w$-simple-minded systems, for $w \geq 1$) gives simple-minded collections (resp. $w$-simple-minded systems) under mild conditions, in the process providing a unified proof of results of A. Dugas and P. Jorgensen. Finally, we show that under mild conditions, mutation of simple-minded collections is compatible with mutation of $w$-simple-minded systems via a singularity category construction due to H. Jin. |
| title | Simple tilts of length hearts and simple-minded mutation |
| topic | Representation Theory Algebraic Geometry Category Theory 18G80, 14F08, 16E35 |
| url | https://arxiv.org/abs/2401.02947 |