Frobenius liftable hypersurfaces

2025/07/16 by Tatsuro Kawakami, Supravat Sarkar, Kawakami, Tatsuro +3
Computer Science · Mathematics · #13A35 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2507.12198

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

Let D be a reduced divisor in \mathbb Pⁿ_k for an algebraically closed field k of positive characteristic p > 0. We prove that if (\mathbb Pⁿ_k, 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\colon Y→ X onto a smooth projective complex variety X of Picard rank 1 such that (Y, f^-1(D)_red) is a toric pair, then X is the projective space and D is a toric divisor.

Citations

• Liftability and vanishing theorems for Fano threefolds in positive characteristic I
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Related

• Global Frobenius Liftability I
• Frobenius morphisms over Z/p² and Bott vanishing
• Liftability of singularities and their Frobenius morphism modulo p²
• A characterization of toric varieties in characteristic p
• On Smooth Divisors of a Projective Hypersurface