| An enriched structureo on a a nodal curve over a (separably closed) field is a special collection of line bundles which combine combinatorial and geometric information. Enriched structures were first defined in the PhD thesis of Laila Maino, where she also constructed a coarse moduli space. They have played a role in the study of degenerating jacobians and limit linear series. We will explain how to define an enriched structure on a nodal curve over an arbitrary base scheme, and construct a fine moduli stack. We will then explain how to compactify this, by replacing line bundles by suitable torsion free sheaves. If time allows, we will discuss applications to the double ramification cycle. This is joint work with Owen Biesel, see arXiv 1607.08835. |