Birational geometry of del Pezzo surfaces of degree 4
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908728465293312 |
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| author | Shramov, Constantin Trepalin, Andrey |
| author_facet | Shramov, Constantin Trepalin, Andrey |
| contents | It is known that any Mori fiber space birational to a minimal smooth del Pezzo surface $S$ of degree $4$ is either a del Pezzo surface of degree $4$ itself, or a smooth cubic surface with a structure of a relatively minimal conic bundle. We show that any del Pezzo surface of degree $4$ birational to $S$ is actually isomorphic to $S$. Also, we sketch an equivariant version of this fact. On the way, we review the biregular classification of del Pezzo surfaces of degree $4$ obtained by A. N. Skorobogatov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Birational geometry of del Pezzo surfaces of degree 4 Shramov, Constantin Trepalin, Andrey Algebraic Geometry It is known that any Mori fiber space birational to a minimal smooth del Pezzo surface $S$ of degree $4$ is either a del Pezzo surface of degree $4$ itself, or a smooth cubic surface with a structure of a relatively minimal conic bundle. We show that any del Pezzo surface of degree $4$ birational to $S$ is actually isomorphic to $S$. Also, we sketch an equivariant version of this fact. On the way, we review the biregular classification of del Pezzo surfaces of degree $4$ obtained by A. N. Skorobogatov. |
| title | Birational geometry of del Pezzo surfaces of degree 4 |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.19660 |