Bisecant and trisecant curves on ruled surfaces

In this paper, we study numerical classes of integral curves on a ruled surface P(E) associated to a stable bundle E. The nef cone of a ruled surface is generated by the classes of a minimal section C0 and a fiber f. We compute the smallest integer b such that the class kC0+bf contains a multisecant curve for k=2 and 3. Also we find its consequence on the Lange stability of SymkE.