  Let $(E,V)$ be a general generated coherent system of type $(n,d,n+m)$ on a
general non-singular irreducible complex projective curve. A conjecture of D.
C. Butler relates the semistability of $E$ to the semistability of the kernel
of the evaluation map $V\otimes \mathcal{O}_X\to E$. The aim of this paper is
to obtain results on the existence of generated coherent systems and use them
to prove Butler's Conjecture in some cases. The strongest results are obtained
for type $(2,d,4)$, which is the first previously unknown case.

Algebraic Geometry