  Let $C$ be a smooth irreducible projective curve of genus $g$ and $L$ a line
bundle of degree $d$ generated by a linear subspace $V$ of $H^0(L)$ of
dimension $n+1$. We prove a conjecture of D. C. Butler on the semistability of
the kernel of the evaluation map $V\otimes{\mathcal O}_C\to L$ and obtain new
results on the stability of this kernel. The natural context for this problem
is the theory of coherent systems on curves and our techniques involve wall
crossing formulae in this theory.
