# IJPAM: Volume 21, No. 4 (2005)

RANK TWO VECTOR BUNDLES AND
SPECIAL RULED SURFACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract.Let be a smooth and connected projective curve and a rank two vector bundle on . Is there such that and is spanned ? Describe all such pairs (at least under certain assumptions on and ). Here we give complete results when is unstable and partial results when is stable and  general '' in its stratum for the stratification given by the order of stability.