Terminal Fano four folds in low codimension
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
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| _version_ | 1866909662047109120 |
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| author | Qureshi, Muhammad Imran |
| author_facet | Qureshi, Muhammad Imran |
| contents | We construct well-formed and quasismooth terminal Fano 4-folds of index 1 in low codimension containing at worst isolated orbifold points. We provide a certain classification of these varieties where their images under the anitcanonical embedding can be described as codimension 2, 3, or 4 subvarieties of some weighted projective space. In particular, we focus on isolated terminal Fano 4-folds that either have an empty linear system or a relatively large one, but whose linear section is not an isolated canonical Calabi--Yau 3-fold. In total, we classify 95 families of terminal Fano 4-folds of the first type and 32 families of the second type. We also describe our algorithmic approach and the pivotal role of computer algebra in our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Terminal Fano four folds in low codimension Qureshi, Muhammad Imran Algebraic Geometry We construct well-formed and quasismooth terminal Fano 4-folds of index 1 in low codimension containing at worst isolated orbifold points. We provide a certain classification of these varieties where their images under the anitcanonical embedding can be described as codimension 2, 3, or 4 subvarieties of some weighted projective space. In particular, we focus on isolated terminal Fano 4-folds that either have an empty linear system or a relatively large one, but whose linear section is not an isolated canonical Calabi--Yau 3-fold. In total, we classify 95 families of terminal Fano 4-folds of the first type and 32 families of the second type. We also describe our algorithmic approach and the pivotal role of computer algebra in our results. |
| title | Terminal Fano four folds in low codimension |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.21958 |