On a combinatorial description of the Gorenstein index for varieties with torus action
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916383575506944 |
|---|---|
| author | Iber, Philipp Reinert, Eva Wrobel, Milena |
| author_facet | Iber, Philipp Reinert, Eva Wrobel, Milena |
| contents | The anticanonical complex is a combinatorial tool that was invented to extend the features of the Fano polytope from toric geometry to wider classes of varieties. In this note we show that the Gorenstein index of Fano varieties with torus action of complexity one (and even more general of the so-called general arrangement varieties) can be read off its anticanonical complex in terms of lattice distances in full analogy to the toric Fano polytope. As an application we give concrete bounds on the defining data of almost homogeneous Fano threefolds of Picard number one having a reductive automorphism group with two-dimensional maximal torus depending on their Gorenstein index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03649 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a combinatorial description of the Gorenstein index for varieties with torus action Iber, Philipp Reinert, Eva Wrobel, Milena Algebraic Geometry 14M25, 14J45, 52B20, 14L30 The anticanonical complex is a combinatorial tool that was invented to extend the features of the Fano polytope from toric geometry to wider classes of varieties. In this note we show that the Gorenstein index of Fano varieties with torus action of complexity one (and even more general of the so-called general arrangement varieties) can be read off its anticanonical complex in terms of lattice distances in full analogy to the toric Fano polytope. As an application we give concrete bounds on the defining data of almost homogeneous Fano threefolds of Picard number one having a reductive automorphism group with two-dimensional maximal torus depending on their Gorenstein index. |
| title | On a combinatorial description of the Gorenstein index for varieties with torus action |
| topic | Algebraic Geometry 14M25, 14J45, 52B20, 14L30 |
| url | https://arxiv.org/abs/2409.03649 |