High degree special ruled surfaces on curves with general moduli

Abstract. Fix integers g ≥ 3 and d ≥ 6g − 4. Here we describe the irreducible components of the set of all triples (C,E, V), where C is a smooth genus g curve with general moduli, E is a rank 2 vector bundle on C with degree d and V is a linear subspace of H0(C,E) such that dim(V) = d + 2 − 2g, V spans E and the morphism P(E) → Pd−2g+1 induced by V is birational onto its image. For another proof (and more) see arXiv:math/0809.0373