Coherent systems and BGN extensions on nodal reducible curves

Abstract

Let $(C,\underline{w})$ 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 $(\underline{w},\alpha )$-stable coherent systems stabilize for large $\alpha$ and we generalize several results known for the irreducible case when we chose a good polarization. Then, we study in details the components of moduli spaces containing coherent systems arising from locally free sheaves.

21 pages

References in corpus (3)

• On kernel bundles over reducible curves with a node
• Coherent systems on curves of compact type
• Nodal curves and polarizations with good properties