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imperfect fields

Journal of the Institute of Mathematics of Jussieu (1)

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UNIRATIONALITY AND GEOMETRIC UNIRATIONALITY FOR HYPERSURFACES IN POSITIVE CHARACTERISTICS
Part of
Keiji Oguiso, Stefan Schröer
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 21 / Issue 5 / September 2022

Published online by Cambridge University Press:

08 March 2021, pp. 1831-1847

Print publication:

September 2022
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Building on work of Segre and Kollár 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 behavior holds for certain cubic surfaces in characteristic $p=2$ .