Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.18134 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910918779076608 |
|---|---|
| author | Choi, Suyoung Jang, Hyeontae Vallée, Mathieu |
| author_facet | Choi, Suyoung Jang, Hyeontae Vallée, Mathieu |
| contents | We classify all complete non-singular toric varieties with Picard number four via a combinatorial framework based on fanlike simplicial spheres and characteristic maps. This classification yields $59$ fanlike seeds with Picard number four, along with all toric manifolds supported by them. As a consequence, we resolve a conjecture of Gretenkort, Kleinschmidt, and Sturmfels by presenting the first known examples of toric manifolds supported by neighborly polytopes. We also answer a question of Batyrev concerning minimal non-faces of such spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete non-singular toric varieties with Picard number 4 Choi, Suyoung Jang, Hyeontae Vallée, Mathieu Algebraic Geometry 57S12 We classify all complete non-singular toric varieties with Picard number four via a combinatorial framework based on fanlike simplicial spheres and characteristic maps. This classification yields $59$ fanlike seeds with Picard number four, along with all toric manifolds supported by them. As a consequence, we resolve a conjecture of Gretenkort, Kleinschmidt, and Sturmfels by presenting the first known examples of toric manifolds supported by neighborly polytopes. We also answer a question of Batyrev concerning minimal non-faces of such spheres. |
| title | Complete non-singular toric varieties with Picard number 4 |
| topic | Algebraic Geometry 57S12 |
| url | https://arxiv.org/abs/2504.18134 |