Moduli spaces of vector bundles on a singular rational ruled surface

Abstract

We study moduli spaces M_X(r,c₁,c₂) parametrizing slope semistable vector bundles of rank r and fixed Chern classes c₁,c₂ on a ruled surface whose base is a rational nodal curve. We show that under certain conditions, these moduli spaces are irreducible, smooth and rational (when non-empty). We also prove that they are non-empty in some cases. We show that for a rational ruled surface defined over real numbers, the moduli space M_X(r,c₁,c₂) is rational as a variety defined over R.