Surfaces defined by pairs of polynomials
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914031573401600 |
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| author | Gvirtz-Chen, Damián Skorobogatov, Alexei |
| author_facet | Gvirtz-Chen, Damián Skorobogatov, Alexei |
| contents | We prove that the Brauer group of the generic diagonal surface of arbitrary degree is trivial. The same method is applied to surfaces whose equation can be written as the sum of two bilinear forms. This uses a general criterion for the triviality of the transcendental Brauer group of an isotrivial variety. We determine the field of definition of the geometric Picard group of the Fermat surface of arbitrary degree, thus finishing work of Shioda and Aoki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08632 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Surfaces defined by pairs of polynomials Gvirtz-Chen, Damián Skorobogatov, Alexei Algebraic Geometry 14F22, 14Q10 We prove that the Brauer group of the generic diagonal surface of arbitrary degree is trivial. The same method is applied to surfaces whose equation can be written as the sum of two bilinear forms. This uses a general criterion for the triviality of the transcendental Brauer group of an isotrivial variety. We determine the field of definition of the geometric Picard group of the Fermat surface of arbitrary degree, thus finishing work of Shioda and Aoki. |
| title | Surfaces defined by pairs of polynomials |
| topic | Algebraic Geometry 14F22, 14Q10 |
| url | https://arxiv.org/abs/2305.08632 |