Enriques' characterization of Abelian surfaces in positive characteristic

Jefferson Baudin; Gebhard Martin

Enriques' characterization of Abelian surfaces in positive characteristic

Algebraic Geometry 2026-05-20 v1

Authors: Jefferson Baudin , Gebhard Martin

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.

Keywords

Enriques characterization Abelian surfaces positive characteristic smooth projective surfaces birational equivalence

Cite

@article{arxiv.2605.20010,
  title  = {Enriques' characterization of Abelian surfaces in positive characteristic},
  author = {Jefferson Baudin and Gebhard Martin},
  journal= {arXiv preprint arXiv:2605.20010},
  year   = {2026}
}

Comments

12 pages, comments welcome

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