Restriction of stable rank two vector bundles in arbitrary characteristic

Details Restriction of stable rank two vector bundles in arbitrary characteristic Restriction of stable rank two vector bundles in arbitrary characteristic

1999-04-20

arxiv.org/abs/math/9904102v1

Mathematics

Algebraic Geometry

LaTeX document, 16 pages, no figures

Scientific paper

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 $\Delta(E).H^{\dim(X)-2}$ 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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