Cubic fourfolds of discriminant 24 and rationality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916470923984896 |
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| author | Hassett, Brendan |
| author_facet | Hassett, Brendan |
| contents | Cubic fourfolds of discriminant 24 contain special codimension-two algebraic cycles of degree 6 and self-intersection 20. Such cycles may be represented by singular scrolls or del Pezzo surfaces. A discriminant 24 cubic fourfold gives rise to a twisted surface, consisting of a degree-six K3 surface and a two-torsion element of its Brauer group. We show that the cubic fourfold is rational if the Brauer class vanishes. This yields a countably-infinite collection of new examples of rational cubic fourfolds, each of codimension two in moduli. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_04222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cubic fourfolds of discriminant 24 and rationality Hassett, Brendan Algebraic Geometry 14E08, 14J35, 14J26, 14J28 Cubic fourfolds of discriminant 24 contain special codimension-two algebraic cycles of degree 6 and self-intersection 20. Such cycles may be represented by singular scrolls or del Pezzo surfaces. A discriminant 24 cubic fourfold gives rise to a twisted surface, consisting of a degree-six K3 surface and a two-torsion element of its Brauer group. We show that the cubic fourfold is rational if the Brauer class vanishes. This yields a countably-infinite collection of new examples of rational cubic fourfolds, each of codimension two in moduli. |
| title | Cubic fourfolds of discriminant 24 and rationality |
| topic | Algebraic Geometry 14E08, 14J35, 14J26, 14J28 |
| url | https://arxiv.org/abs/2411.04222 |