Coherent systems and BGN extensions on nodal reducible curves

Abstract

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 (w, α)-stable coherent systems stabilize for large α 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.

Higher rank Brill—Noether theory and coherent systems open questions

“…For a reducible nodal curve, the components of the moduli space M (n, d) were determined in [100,101] together with a useful criterion for the existence of stable bundles. For recent work on coherent systems on reducible nodal curves, see [30,31]. The failure of Butler's conjecture on a reducible nodal curve with 2 components and one node is discussed in [29].…”

Higher rank Brill-Noether theory and coherent systems: Open questions

“…For a reducible nodal curve, the components of the moduli space M(n, d) were determined in [Tei91b,Tei95] together with a useful criterion for the existence of stable bundles. For recent work on coherent systems on reducible nodal curves, see [BrF20b,BrF21]. The failure of Butler's conjecture on a reducible nodal curve with 2 components and one node is discussed in [BrF20a].…”