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This is a Quantitative Study study.

October 12, 2025Open Access

On F-pure thresholds and quasi-F-purity of hypersurfaces

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Quasi-F-pure singularities exhibit an F-pure threshold of 1 - 1/p, highlighting a significant relationship.
This finding extends previous work on Calabi-Yau cases, enhancing understanding of purity in singularities.
Classification of (quasi)-F-purity in Fermat hypersurfaces contributes to broader complex geometry studies.
Insights into F-pure thresholds may lead to new approaches in algebraic geometry, deepening existing theories.

Implication

Research reveals that isolated quasi-homogeneous hypersurface singularities show quasi-F-purity, suggesting distinct F-pure thresholds.

Abstract

We show that quasi-F-pure but not F-pure isolated quasi-homogeneous hypersurface singularities necessarily have F-pure threshold 1 - 1/p. This extends work of Bhatt and Singh beyond the Calabi-Yau case. We also classify the (quasi)-F-purity of Fermat hypersurfaces.

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Cite This Study

Garzella et al. (2025) studied this question.

synapsesocial.com/papers/68ebffcfdef9fcb308ff26df https://doi.org/10.48550/arxiv.2509.06211

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Implication

Research reveals that isolated quasi-homogeneous hypersurface singularities show quasi-F-purity, suggesting distinct F-pure thresholds.

On F-pure thresholds and quasi-F-purity of hypersurfaces

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Implication

Abstract

Discussion

Cite This Study

On F-pure thresholds and quasi-F-purity of hypersurfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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