Rational points on even dimensional Fermat cubics
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911918991605760 |
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| author | Massarenti, Alex |
| author_facet | Massarenti, Alex |
| contents | We show that even dimensional Fermat cubic hypersurfaces are rational over any field of characteristic different from three by producing explicit rational parametrizations given by polynomials of low degree. As a byproduct of our rationality constructions we get estimates on the number of their rational points over a number field, and a class of quadro-cubic Cremona correspondences of even dimensional projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07223 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational points on even dimensional Fermat cubics Massarenti, Alex Algebraic Geometry Number Theory Rings and Algebras Primary 12F20, 12E10, 14E08, 14M20, 12F10, Secondary 14G05 We show that even dimensional Fermat cubic hypersurfaces are rational over any field of characteristic different from three by producing explicit rational parametrizations given by polynomials of low degree. As a byproduct of our rationality constructions we get estimates on the number of their rational points over a number field, and a class of quadro-cubic Cremona correspondences of even dimensional projective spaces. |
| title | Rational points on even dimensional Fermat cubics |
| topic | Algebraic Geometry Number Theory Rings and Algebras Primary 12F20, 12E10, 14E08, 14M20, 12F10, Secondary 14G05 |
| url | https://arxiv.org/abs/2406.07223 |