  We prove a smoothness result for spaces of linear series with prescribed
ramification on twice-marked elliptic curves. In characteristic 0, we then
apply the Eisenbud-Harris theory of limit linear series to deduce a new proof
of the Gieseker-Petri theorem, along with a generalization to spaces of linear
series with prescribed ramification at up to two points. Our main calculation
involves the intersection of two Schubert cycles in a Grassmannian associated
to almost-transverse flags.
