We describe a closed immersion from each representation space of a type A
quiver with bipartite (i.e., alternating) orientation to a certain opposite
Schubert cell of a partial flag variety. This "bipartite Zelevinsky map"
restricts to an isomorphism from each orbit closure to a Schubert variety
intersected with the above-mentioned opposite Schubert cell. For type A quivers
of arbitrary orientation, we give the same result up to some factors of general
linear groups.
These identifications allow us to recover results of Bobinski and Zwara;
namely we see that orbit closures of type A quivers are normal, Cohen-Macaulay,
and have rational singularities. We also see that each representation space of
a type A quiver admits a Frobenius splitting for which all of its orbit
closures are compatibly Frobenius split.