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arXiv · 2508.03623

Nonrational varieties with unirational parametrizations of coprime degrees

Song Yang·Xun Yu·Zigang Zhu
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Abstract

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.

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Song Yang, Xun Yu, Zigang Zhu. 2025-08-05. Nonrational varieties with unirational parametrizations of coprime degrees. https://arxiv.org/abs/2508.03623

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