The Gieseker–Petri theorem and imposed ramification

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.