Coherent systems and BGN extensions on nodal reducible curves

Let (C,w) be a polarized nodal reducible curve. In this paper, we consider coherent systems of type (r,d,k) on C with k < r. We prove that the moduli spaces of -stable coherent systems stabilize for large α and we generalize several results known for the irreducible case when we choose a good polarization. Then, we study in detail the components of moduli spaces containing coherent systems arising from locally free sheaves.