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On $F$-pure inversion of adjunction

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arxiv 2305.17591 v1 pith:PWPQAUGJ submitted 2023-05-27 math.AG math.AC

Thomas Polstra , Austyn Simpson , Kevin Tucker This is my paper · ORCID
classification math.AGmath.AC
keywords adjunctioninversioncharacteristicdeltagivepairspurityanalysis
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abstract

We analyze adjunction and inversion of adjunction for the $F$-purity of divisor pairs in characteristic $p > 0$. In this vein, we give a complete answer for principal divisors under $\mathbb{Q}$-Gorenstein assumptions but without divisibility restrictions on the index. We also give a detailed analysis relating the $F$-purity of the pairs $(R,\Delta + D)$ and that of $(R_D, \text{Diff}_D(\Delta))$ motivated by Kawakita's log canonical inversion of adjunction via reduction to prime characteristic.

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Cited by 1 Pith paper

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  1. Pathological MMP singularities as $\alpha_p$-quotients

    math.AG 2025-01 conditional novelty 8.0 of 10

    For every positive characteristic, the author constructs non-S3 terminal singularities of dimension p+1 and stable families with klt, Cohen-Macaulay, F-injective general fibers but non-S2 special fibers.

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