Generic ordinarity for semi-stable fibration

2008/05/26 by Junmyeong Jang, Jang, Junmyeong
Mathematics · #11G25 #14J20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0805.3982

openalex publication_date 2008/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we proved that, for a semi-stable fibration of a proper smooth surface to a proper smooth curve over a field of positive characteristic, if the generic fiber is ordinary, then the semi-positivity theorem holds. As an application, we constrcuted a counterexample to Parshin's conjecture on the Miyaoka-Yau inequality.

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