Coherent systems and BGN extensions on nodal reducible curves

TL;DR

This paper studies the stability and structure of coherent systems on polarized nodal reducible curves, extending known results from irreducible cases and analyzing moduli space components related to locally free sheaves.

Contribution

It generalizes stability results for coherent systems on reducible curves and analyzes moduli space components associated with locally free sheaves.

Findings

Moduli spaces stabilize for large lpha.

Generalization of irreducible case results to reducible curves.

Detailed analysis of components containing locally free sheaves.

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.