Coherent systems and BGN extensions on nodal reducible curves

Abstract

Let [Formula: see text] be a polarized nodal reducible curve. In this paper, we consider coherent systems of type [Formula: see text] on [Formula: see text] with [Formula: see text]. We prove that the moduli spaces of [Formula: see text]-stable coherent systems stabilize for large [Formula: see text] 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.