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On Frobenius liftability of surface singularities

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arxiv 2402.08152 v1 pith:TB7IDXW6 submitted 2024-02-13 math.AG

Tatsuro Kawakami , Teppei Takamatsu This is my paper · ORCID
classification math.AG
keywords surfacecharacteristicpairspurebogomolov-sommeseconsequencedoubleextension
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abstract

We show that a plt surface singularity $(P\in X,B)$ is $F$-liftable if and only if it is $F$-pure and is not a rational double point of type $E_8^1$ in characteristic $p=5$. As a consequence, we prove the logarithmic extension theorem for $F$-pure surface pairs and Bogomolov-Sommese vanishing for globally $F$-split surface pairs. These results were previously known to hold in characteristic $p>5$.

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  1. Frobenius liftable hypersurfaces

    math.AG 2025-07 accept novelty 7.0 of 10

    Frobenius-liftable reduced divisors in projective space are exactly toric divisors, up to automorphism.

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