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On $F$-pure inversion of adjunction

· 2023 · math.AG · arXiv 2305.17591

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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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math.AG 1

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2025 1

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CONDITIONAL 1

representative citing papers

Pathological MMP singularities as $\alpha_p$-quotients

math.AG · 2025-01-02 · conditional · novelty 8.0

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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  • Pathological MMP singularities as $\alpha_p$-quotients math.AG · 2025-01-02 · conditional · none · ref 11 · internal anchor

    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.