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 \(V \subset H^0(E)\) of dimension \(k\). Moduli spaces of stable coherent systems have been introduced by King and Newstead and depend on a real parameter \(\alpha\). We show that when \(k \geq r\), these moduli spaces coincide for \(\alpha\) 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.