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.
ACKNOWLEDGMENT
The author is grateful to the referee for pointing out several inaccuracies in the original version of this article.
Notes
Communicated by R. Piene.