Restrictions of rank-2 semistable vector bundles on surfaces in positive characteristic
Let \(S\) be a smooth projective surface over an algebraically closed field \(K\) with \(\text{char}(k)= p>0\), \({\mathcal O}_S(1)\) a very ample line bundle on \(S\) and \(E\) a rank-2 \({\mathcal O}_S(1)\)-semistable vector bundle on \(S\). Using ideas of \textit{L. Ein} [Math. Ann. 254, 53-72 (1980; Zbl 0431.14003)] and \textit{H. Flenner} [Comment. Math. Helv. 59, 635-650 (1984; Zbl 0599.14015)] the author finds an effective bound \(d_0\) such that if \(d\geq d_0\) the restriction \(E\mid C\) of \(E\) to a general member \(C\in|{\mathcal O}(d)|\) is semistable. In this way one gets an effective version in positive characteristic (in the case of surfaces) of a theorem of \textit{V. B. Mehta} and \textit{A. Ramanathan} [Math. Ann. 258, 213-224 (1982; Zbl 0473.14001)].
scientific article; zbMATH DE number 1344320