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Journal of the Institute of Mathematics of Jussieu (1)

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RATIONALITY OVER NONCLOSED FIELDS OF FANO THREEFOLDS WITH HIGHER GEOMETRIC PICARD RANK
Part of
- Surfaces and higher-dimensional varieties
- Birational geometry
Alexander Kuznetsov, Yuri Prokhorov
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 23 / Issue 1 / January 2024

Published online by Cambridge University Press:

05 August 2022, pp. 207-247

Print publication:

January 2024
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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.