  For an acyclic quiver with three vertices, we consider the canonical
decomposition of a non-Schurian root and associate certain representations of a
generalized Kronecker quiver. These representations correspond to points
contained in the intersection of two subvarieties of a Grassmannian and give
rise to representations of the original quiver, preserving indecomposability.
We show that these subvarieties intersect using Schubert calculus. Provided
that the intersection contains a Schurian representation, it already contains
an open subset of Schurian representations whose dimension is what we expect by
Kac's Theorem.
