Nonrational varieties with unirational parametrizations of coprime degrees
Algebraic Geometry
2025-08-08 v2
Abstract
We show that there exists a -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.
Cite
@article{arxiv.2508.03623,
title = {Nonrational varieties with unirational parametrizations of coprime degrees},
author = {Song Yang and Xun Yu and Zigang Zhu},
journal= {arXiv preprint arXiv:2508.03623},
year = {2025}
}
Comments
10 pages, some minor changes (a few remarks and references are added)