Enriques' characterization of Abelian surfaces in positive characteristic
Abstract
Extending Enriques' characterization to algebraically closed fields of characteristic p ≥ 7, we show that every smooth projective surface X with h1(X, OX) = 2 and p1(X) = p2(X) = 1 is birational to an Abelian surface. This characterization fails if p ≤ 5, and we give a sharp alternative.
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