# IJPAM: Volume 20, No. 2 (2005)

VECTOR SUBSPACES OF SECTIONS AND
STABLE COHERENT SYSTEMS ON CURVES

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, a non-trivial rank vector bundle on and an -dimensional linear subspace of spanning . Assume that is unramified. Fix a general -dimensional linear subspace of . Then:

(a) for a general -dimensional linear subspace of the evaluation map is injective and with locally free cokernel;

(b) for every -dimensional linear subspace of the evaluation map is injective as a map of sheaves;

(c) there is a non-empty family of the hyperplanes of such that the evaluation map is injective as a map of sheaves, but it has a non-locally free cokernel if and only if ; at each the fiber at of has rank at least ; the saturation of in has degree one; has pure dimension .