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arXiv · 2605.20010

Enriques' characterization of Abelian surfaces in positive characteristic

Jefferson Baudin·Gebhard Martin
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Abstract

Extending Enriques' characterization to algebraically closed fields of characteristic $p \geq 7$, we show that every smooth projective surface $X$ with $h^1(X, \mathcal{O}_X) = 2$ and $p_1(X) = p_2(X) = 1$ is birational to an Abelian surface. This characterization fails if $p \leq 5$, and we give a sharp alternative.

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Jefferson Baudin, Gebhard Martin. 2026-05-19. Enriques' characterization of Abelian surfaces in positive characteristic. https://arxiv.org/abs/2605.20010

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