  We study sheaves E on a smooth projective curve X which are minimal with
respect to the property that $h^0(E \otimes L) >0$ for all line bundles L of
degree zero. We show that these sheaves define ample divisors D(E) on the
Picard torus Pic(X). Next we classify all minimal sheaves of rank one and two.
As an application we show that the moduli space parameterizing rank two bundles
of odd degree can be obtained as a Quot scheme.
