Restriction of stable rank two vector bundles in arbitrary\n characteristic

1999/04/20 by Georg Hein, Hein, Georg
Mathematics · #14D20 #14D22 #14F17 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/9904102

openalex publication_date 1999/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth variety defined over an algebraically closed field of\narbitrary characteristic and O_X(H) be a very ample line bundle on X. We\nshow that for a semistable X-bundle E of rank two, there exists an integer\nm depending only on \Δ(E).H^\dim(X)-2 and H^\dim(X) such that the\nrestriction of E to a general divisor in |mH| is again semistable. As\ncorollaries we obtain boundedness results, and weak versions of Bogomolov's\ntheorem and Kodaira's vanishing theorem for surfaces in arbitrary\ncharacteristic.\n

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