Manin's conjecture for the chordal cubic fourfold
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908332463226880 |
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| author | Derenthal, Ulrich |
| author_facet | Derenthal, Ulrich |
| contents | We prove the thin set version of Manin's conjecture for the chordal (or: determinantal) cubic fourfold, which is the secant variety of the Veronese surface. We reduce this counting problem to a result of Schmidt for quadratic points in the projective plane by showing that the chordal cubic fourfold is isomorphic to the symmetric square of the projective plane over the rational numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Manin's conjecture for the chordal cubic fourfold Derenthal, Ulrich Number Theory Algebraic Geometry 11D25 (Primary) 11D45, 14G05 (Secondary) We prove the thin set version of Manin's conjecture for the chordal (or: determinantal) cubic fourfold, which is the secant variety of the Veronese surface. We reduce this counting problem to a result of Schmidt for quadratic points in the projective plane by showing that the chordal cubic fourfold is isomorphic to the symmetric square of the projective plane over the rational numbers. |
| title | Manin's conjecture for the chordal cubic fourfold |
| topic | Number Theory Algebraic Geometry 11D25 (Primary) 11D45, 14G05 (Secondary) |
| url | https://arxiv.org/abs/2504.16051 |