Abstract
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.
Funder
HSE University Basic Research Program
Publisher
Cambridge University Press (CUP)
Cited by
3 articles.
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1. Rationality of Fano threefolds over non-closed fields;American Journal of Mathematics;2023-04
2. On higher-dimensional del Pezzo varieties;Известия Российской академии наук. Серия математическая;2023
3. On higher-dimensional del Pezzo varieties;Izvestiya: Mathematics;2023