Resumen de Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view
Moduli spaces of vector bundles on families of non-singular curves are usually compactified by considering (slope)semistable bundles on stable curves. Alternatively, one could consider Hilbert-stable curves in Grassmannians. We study some properties of the latter and compare them with similar properties of curves coming from the former compactification. This leads to a new interpretation of the moduli space of (semi)stable torsion-free sheaves on a fixed nodal curve. One can present it as a quotient of a moduli space of torsion-free sheaves on a variable curve in such a way that each class has a locally-free representative.
