October 15, 2025Open Access

Frobenius liftable hypersurfaces

Puntos clave

Proving that a Frobenius liftable divisor is toric reveals deep geometric properties.
The study shows that an existing finite morphism to a complex variety confines the structure to projective space.
Frobenius liftability modulo p^2 indicates distinctive behaviors for certain hypersurfaces.
Connecting toric properties with morphisms highlights the geometric significance of Picard rank.

Resumen

Let D be a reduced divisor in Pⁿₖ for an algebraically closed field k of positive characteristic p > 0. We prove that if (Pⁿₖ, D) is Frobenius liftable modulo p², then D is a toric divisor. As a corollary, we show that if there exists a finite surjective morphism f Y X onto a smooth projective complex variety X of Picard rank 1 such that (Y, f^-1 (D) ₑ₄₃) is a toric pair, then X is the projective space and D is a toric divisor.

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Cite This Study

Kawakami et al. (Wed,) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba06355674 https://doi.org/https://doi.org/10.48550/arxiv.2507.12198

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