A Mehta–Ramanathan theorem for linear systems with basepoints. Issue 10 (11th January 2016) - Graf, Patrick
Abstract : Let ( X, H ) be a normal complex projective polarized variety and E an H ‐semistable sheaf on X . We prove that the restriction E | C to a sufficiently positive general complete intersection curve C ⊂ X passing through a prescribed finite set of points S ⊂ X remains semistable, provided that at each p ∈ S, the variety X is smooth and the factors of a Jordan–Hölder filtration of E are locally free. As an application, we obtain a generalization of Miyaoka's generic semipositivity theorem.