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arXiv · 2002.09228

Unirationality and geometric unirationality for hypersurfaces in positive characteristics

Keiji Oguiso·Stefan Schröer
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Abstract

Building on work of Segre and Koll'ar on cubic hypersurfaces, we construct over imperfect fields of characteristic p\geq 3 particular hypersurfaces of degree p, which show that geometrically rational schemes that are regular and whose rational points are Zariski dense are not necessarily unirational. A likewise behaviour holds for certain cubic surfaces in characteristic p=2.

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Keiji Oguiso, Stefan Schröer. 2020-02-21. Unirationality and geometric unirationality for hypersurfaces in positive characteristics. https://arxiv.org/abs/2002.09228

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