Geometry and arithmetic of geometrically integral regular del Pezzo surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909897002582016 |
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| author | Bernasconi, Fabio Tanaka, Hiromu |
| author_facet | Bernasconi, Fabio Tanaka, Hiromu |
| contents | We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration onto a curve over an algebraically closed field always admits a section. Moreover, we prove that the total space is rational if the base curve is rational and the anticanonical degree of a fibre is at least five. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry and arithmetic of geometrically integral regular del Pezzo surfaces Bernasconi, Fabio Tanaka, Hiromu Algebraic Geometry We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration onto a curve over an algebraically closed field always admits a section. Moreover, we prove that the total space is rational if the base curve is rational and the anticanonical degree of a fibre is at least five. |
| title | Geometry and arithmetic of geometrically integral regular del Pezzo surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.11378 |