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UNIRATIONALITY AND GEOMETRIC UNIRATIONALITY FOR HYPERSURFACES IN POSITIVE CHARACTERISTICS
Published online by Cambridge University Press: 08 March 2021
Abstract
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 $p=2$ .
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1831 - 1847
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press