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arXiv · 2103.02934

Rationality over non-closed fields of Fano threefolds with higher geometric Picard rank

Alexander Kuznetsov·Yuri Prokhorov
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Abstract

We prove rationality criteria over algebraically non-closed 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 prove stable non-rationality under additional assumptions.

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Alexander Kuznetsov, Yuri Prokhorov. 2021-03-04. Rationality over non-closed fields of Fano threefolds with higher geometric Picard rank. https://arxiv.org/abs/2103.02934

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