A Mehta-Ramanathan theorem for linear systems with basepoints (Q2816985)

Let \(X\) be a normal complex projective variety and \(H\) an ample divisor on \(X\). In [Math. Ann. 258, 213--224 (1982; Zbl 0473.14001)], \textit{V. B. Mehta} and \textit{A. Ramanathan} have shown that for a smooth \(X\) the restriction of an \(H\)-semistable sheaf \(\mathcal{E}\) on \(X\) to a sufficiently positive general complete intersection curve \(C\) remains semistable. In [Comment. Math. Helv. 59, 635--650 (1984; Zbl 0599.14015)], \textit{H. Flenner} obtained a stronger result for arbitrary normal varieties.NEWLINENEWLINEIn the present paper the author considers a complete intersection curve \(C\) that passes through a set \(S\) of points in the smooth locus of \(X\). In the main theorem of the paper, he shows that if \(\mathcal{E}\) is \(H\)-semistable and in addition the factors of a Jordan-Hölder filtration of \(\mathcal{E}\) are locally free then the restriction of \(\mathcal{E}\) on \(C\) is a semistable vector bundle [\textit{A. Langer}, J. Ramanujan Math. Soc. 28A, 287--309 (2013; Zbl 1295.14032)].