Every smooth projective surface X over an algebraically closed field of char p ≥ 7 with h¹(X, O_X) = 2 and p₁(X) = p₂(X) = 1 is birational to an Abelian surface.
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The Artin invariant of a smooth K3 hypersurface is characterized in terms of quasi-F-splitting, yielding an explicit formula.
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Enriques' characterization of Abelian surfaces in positive characteristic
Every smooth projective surface X over an algebraically closed field of char p ≥ 7 with h¹(X, O_X) = 2 and p₁(X) = p₂(X) = 1 is birational to an Abelian surface.
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An explicit formula for the Artin invariant of smooth K3 hypersurfaces
The Artin invariant of a smooth K3 hypersurface is characterized in terms of quasi-F-splitting, yielding an explicit formula.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.