DC MetaData for: Restriction of stable rank two vector bundles in arbitrary characteristic

Georg Hein
Restriction of stable rank two vector bundles in arbitrary characteristic
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:: 14D20 Algebraic moduli problems, moduli of vector bundles, {For analytic moduli problems, See 32G13}; 14D22 Fine and coarse moduli spaces

Abstract: 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).H^dim(X)-2 and H^dim(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.

Keywords: restriction theorems, vector bundle, Bogomolov inequality