An irregular smooth Fano fourfold in positive characteristic

Joe Waldron, Jakub Witaszek

Source record

Source: arXiv

Published: Sep 24, 2026

arXiv: 2609.29924

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Source abstract

We construct an explicit smooth projective Fano fourfold $X$ over an algebraically closed field $k$ of characteristic two with $H^1(X,\mathcal{O}_X)\simeq k$ . Moreover, $X$ does not admit any free rational curve, and so it is not separably uniruled. The example has been constructed using ChatGPT.

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An irregular smooth Fano fourfold in positive characteristic — Mathematical Frontier Network