Automorphism groups and cylindricity of weighted hypersurface Fano threefolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916936766455808 |
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| author | Kim, In-Kyun Kishimoto, Takashi Won, Joonyeong |
| author_facet | Kim, In-Kyun Kishimoto, Takashi Won, Joonyeong |
| contents | It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$ families, $15$ families have the property that general members are irrational, in particular, any of them has a finite automorphism group and is not cylindrical. In the present paper, we will observe the cylindricity and the full automorphism groups of every member in the remaining $20$ families. Moreover, we deal with the cylindricity of their forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automorphism groups and cylindricity of weighted hypersurface Fano threefolds Kim, In-Kyun Kishimoto, Takashi Won, Joonyeong Algebraic Geometry It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$ families, $15$ families have the property that general members are irrational, in particular, any of them has a finite automorphism group and is not cylindrical. In the present paper, we will observe the cylindricity and the full automorphism groups of every member in the remaining $20$ families. Moreover, we deal with the cylindricity of their forms. |
| title | Automorphism groups and cylindricity of weighted hypersurface Fano threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.04367 |