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This is a Quantitative Study study.

October 20, 2025Open Access

Bertini's theorem for F-rational F-pure singularities

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Intersections of F-pure varieties with hyperplanes are also F-pure, ensuring consistency in their properties.
The study reveals a connection between the characteristic and index of a Gorenstein variety with an isolated non-F-regular locus.
Findings contribute to understanding the structural properties of quasi-projective varieties under specific conditions.
Explorations into the implications of F-purity are essential for advancing the theory of singularities in positive characteristic.

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Implication

This research demonstrates that intersections of F-pure varieties with hyperplanes remain F-pure, highlighting implications for Gorenstein varieties with isolated non-F-regular loci.

Cite This Study

Stefani et al. (2025) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1d16 https://doi.org/10.48550/arxiv.2509.04433

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Implication

This research demonstrates that intersections of F-pure varieties with hyperplanes remain F-pure, highlighting implications for Gorenstein varieties with isolated non-F-regular loci.

Bertini's theorem for F-rational F-pure singularities

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Implication

Cite This Study

Bertini's theorem for F-rational F-pure singularities

Key Points

Discussion

Implication

Cite This Study

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