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RATIONALITY OVER NONCLOSED FIELDS OF FANO THREEFOLDS WITH HIGHER GEOMETRIC PICARD RANK
Published online by Cambridge University Press: 05 August 2022
Abstract
We prove rationality criteria over nonclosed fields of characteristic $0$ for five out of six types of geometrically rational Fano threefolds of Picard number $1$ and geometric Picard number bigger than $1$. For the last type of such threefolds, we provide a unirationality criterion and construct examples of unirational but not stably rational varieties of this type.
MSC classification
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- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 1 , January 2024 , pp. 207 - 247
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press
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