2014/05/01 by Lingguang Li, Li, Lingguang, Junchao Shentu +1
Computer Science · Mathematics · #14F17 #14G17 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #math.AG #msc:14F17 #msc:14G17 #msc:14J60
paper · pdf · doi:10.48550/arxiv.1405.0106
To appear in Comptes Rendus Mathématique
openalex publication_date 2014/05/01 · arxiv created 2014/05/27 · arxiv updated 2014/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth projective variety over an algebraically closed field k of characteristic p>0 of dim X≥ 4 and Picard number ρ(X)=1. Suppose that X satisfies Hi(X,Fm*X(\OmgjX)⊗\Ls-1)=0 for any ample line bundle \Ls on X, and any nonnegative integers m,i,j with 0≤ i+j<dim X, where FX:X→ X is the absolute Frobenius morphism. We prove that by procedures combining taking smooth hypersurfaces of dimension ≥ 3 and cyclic covers along smooth divisors, if the resulting smooth projective variety Y has ample (resp. nef) canonical bundle ωY, then \OmgY is strongly stable (resp. strongly semistable) with respect to any polarization.