The Artin invariant of a smooth K3 hypersurface is characterized in terms of quasi-F-splitting, yielding an explicit formula.
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Constructs non-projective complete log canonical surfaces with semi-ample canonical divisors for Kodaira dimensions 0/1/2 and proves automatic projectivity when Kodaira dimension is minus infinity.
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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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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Non-projective complete log canonical surfaces
Constructs non-projective complete log canonical surfaces with semi-ample canonical divisors for Kodaira dimensions 0/1/2 and proves automatic projectivity when Kodaira dimension is minus infinity.
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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.