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October 20, 2025Open Access

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

Key Points

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.

Abstract

Let k be an algebraically closed field of characteristic p>0, and let Xⁿₖ be a quasi-projective variety that is F-rational and F-pure. We prove that if H Pⁿₖ is a general hyperplane, then X H is also F-rational and F-pure. Of related but independent interest, we present a relationship between the characteristic and index of a Q-Gorenstein variety with isolated non-F-regular locus which is F-pure but not F-regular.

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

Key Points

Abstract

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