Coherent systems on curves of compact type

Let C be 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 components of C and a k-dimensional subspace V of H^0(E). Moduli spaces of stable coherent systems have been introduced by King and Newstead and depend on a real parameter. We show that when k > r-1, these moduli spaces coincide for the parameter big enough. Then we deal with the case k = r+1: when the degree 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.