Isotrivial elliptic surfaces in positive characteristic
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917928098594816 |
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| author | Fong, Pascal Maccan, Matilde |
| author_facet | Fong, Pascal Maccan, Matilde |
| contents | We study relatively minimal surfaces equipped with a strongly isotrivial elliptic fibration in positive characteristic by means of the notion of equivariantly normal curves introduced and developed recently by Brion. Such surfaces are isomorphic to a contracted product $E\times^G X$, where $E$ is an elliptic curve, $G$ is a finite subgroup scheme of $E$ and $X$ is a $G$-normal curve. Using this description, we compute their Betti numbers to determine their birational classes. This allow us to complete the classification of maximal automorphism groups of surfaces in any characteristic. When $G$ is diagonalizable, we compute additional invariants to study the structure of their Picard schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isotrivial elliptic surfaces in positive characteristic Fong, Pascal Maccan, Matilde Algebraic Geometry 14J27, 14L15, 14L30 We study relatively minimal surfaces equipped with a strongly isotrivial elliptic fibration in positive characteristic by means of the notion of equivariantly normal curves introduced and developed recently by Brion. Such surfaces are isomorphic to a contracted product $E\times^G X$, where $E$ is an elliptic curve, $G$ is a finite subgroup scheme of $E$ and $X$ is a $G$-normal curve. Using this description, we compute their Betti numbers to determine their birational classes. This allow us to complete the classification of maximal automorphism groups of surfaces in any characteristic. When $G$ is diagonalizable, we compute additional invariants to study the structure of their Picard schemes. |
| title | Isotrivial elliptic surfaces in positive characteristic |
| topic | Algebraic Geometry 14J27, 14L15, 14L30 |
| url | https://arxiv.org/abs/2405.11602 |