Coherent systems on curves of compact type

Let C be a polarized nodal curve of compact type. In this paper we study coherent systems (E,V) on C given by a depth one sheaf E having rank r on each irreducible component of C and a subspace V⊂H0(E) of dimension k. Moduli spaces of stable coherent systems have been introduced by King and Newstead (1995) and depend on a real parameter α. We show that when k≥r, these moduli spaces coincide for α big enough. Then we deal with the case k=r+1: when the degrees of the restrictions of E are big enough we are able to describe an irreducible component of this moduli space by using the dual span construction.