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arXiv · 2406.07223

Rational points on even dimensional Fermat cubics

Alex Massarenti
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Abstract

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.

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Alex Massarenti. 2024-06-11. Rational points on even dimensional Fermat cubics. https://arxiv.org/abs/2406.07223

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