  In this article we determine exactly which line bundles on elliptic ruled
surface X are normally presented. In particular we see that numerical classes
of normally presented divisors form a convex set. (recall that Num(X) is
generated by the class of a minimal section C_0 and by the class of a fiber f
and that C_0 is ample.) As a corollary of the above result we show that Mukai's
conjecture is true for the normal presentation of the it adjoint linear series
for an elliptic ruled surface. In section 5 of this article, we show that if L
is normally presented on X then the homogeneous coordinate ring associated to L
is Koszul. We also give a new proof of the following result due to Butler: if
deg(L) \geq 2g+2 on a curve X of genus g, then L embeds X with Koszul
homogeneous coordinate ring.
