Abstract
Let X be a smooth variety defined over an algebraically closed field of arbitrary characteristic and 𝒪 X (H) be a very ample line bundle on X. We show that for a semistable X-bundle E of rank two, there exists an integer m depending only on Δ(E) · H dim(X)−2 and H dim(X) such that the restriction of E to a general divisor in |mH| is again semistable. As corollaries, we obtain boundedness results, and weak versions of Bogomolov's Theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic.
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