1999-06-02Buch DOI: 10.18452/2668
Restriction of stable rank two vector bundles in arbitrary characteristic
Let X be a smooth variety defined over an algebraically closed field of arbitrary characteristic and H be a very ample divisor on X. We show that for a semistable X-bundle E of rank two, there exists an integer m depending only on Delta(E).Hdim(X)-2 and Hdim(X) such that the restriction of E to a general divisor in the linear system |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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