Log terminal singularities, platonic tuples and iteration of Cox rings
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2017
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918083749216256 |
|---|---|
| author | Arzhantsev, Ivan Braun, Lukas Hausen, Juergen Wrobel, Milena |
| author_facet | Arzhantsev, Ivan Braun, Lukas Hausen, Juergen Wrobel, Milena |
| contents | Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of surface singularities. We extend this picture to log terminal singularities in any dimension coming with a torus action of complexity one. In this setting, the previously finite groups become solvable torus extensions. As explicit examples, we investigate compound du Val threefold singularities. We give a complete classification and exhibit all the possible chains of iterated Cox rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_03627 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Log terminal singularities, platonic tuples and iteration of Cox rings Arzhantsev, Ivan Braun, Lukas Hausen, Juergen Wrobel, Milena Algebraic Geometry 14L30, 14L32, 14E15, 14B05 Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of surface singularities. We extend this picture to log terminal singularities in any dimension coming with a torus action of complexity one. In this setting, the previously finite groups become solvable torus extensions. As explicit examples, we investigate compound du Val threefold singularities. We give a complete classification and exhibit all the possible chains of iterated Cox rings. |
| title | Log terminal singularities, platonic tuples and iteration of Cox rings |
| topic | Algebraic Geometry 14L30, 14L32, 14E15, 14B05 |
| url | https://arxiv.org/abs/1703.03627 |