Unbounded negativity on rational surfaces in positive characteristic

2021/03/03 by Raymond Cheng, Cheng, Raymond, Remy van Dobben de Bruyn +1
Mathematics · #14C17 (primary) #14C20 #14E05 (secondary) #14G17 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2103.02172

openalex publication_date 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give explicit blowups of the projective plane in positive characteristic that contain smooth rational curves of arbitrarily negative self-intersection, showing that the Bounded Negativity Conjecture fails even for rational surfaces in positive characteristic.

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