Simple bases for quiver representations arising from limit linear series.

We explore the existence of simple bases for certain special representations of quivers arising from degenerations of linear series on nodal curves. The existence of a simple basis implies that the representation decomposes into representations of dimension one and simplifies the calculus of the multivariate Hilbert polynomial of the quiver Grassmannian associated to the representation. For these representations of quivers, we characterize the existence of a simple basis by a local condition. This paper is the first of two, aimed to study the linked projective space of a limit linear series.