Nonrational varieties with unirational parametrizations of coprime degrees
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911095740956672 |
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| author | Yang, Song Yu, Xun Zhu, Zigang |
| author_facet | Yang, Song Yu, Xun Zhu, Zigang |
| contents | We show that there exists a $2$-dimensional family of smooth cubic threefolds admitting unirational parametrizations of coprime degrees. This together with Clemens--Griffiths' work solves the long standing open problem whether there exists a nonrational variety with unirational parametrizations of coprime degrees. Our proof uses a new approach, called the Noether--Cremona method, for determining the rationality of quotients of hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonrational varieties with unirational parametrizations of coprime degrees Yang, Song Yu, Xun Zhu, Zigang Algebraic Geometry We show that there exists a $2$-dimensional family of smooth cubic threefolds admitting unirational parametrizations of coprime degrees. This together with Clemens--Griffiths' work solves the long standing open problem whether there exists a nonrational variety with unirational parametrizations of coprime degrees. Our proof uses a new approach, called the Noether--Cremona method, for determining the rationality of quotients of hypersurfaces. |
| title | Nonrational varieties with unirational parametrizations of coprime degrees |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.03623 |