Fine Compactified Moduli of Enriched Structures on Stable Curves

Fine Compactified Moduli of Enriched Structures on Stable Curves Synopsis

"Enriched structures on stable curves over fields were defined by Maino in the late 1990s, and have played an important role in the study of limit linear series and degenerating jacobians. In this paper we solve three main problems: we give a definition of enriched structures on stable curves over arbitrary base schemes, and show that the resulting fine moduli problem is representable; we show that the resulting object has a universal property in terms of Neron models; and we construct a compactification of our stack of enriched structures"--.