| n order to extend the notion of limit linear series to any reducible stable curve X, we introduce the notion of enriched structure on X.;Let X be a stable curve with irreducible components ;In this paper we study the dependence of an enriched structure on the family inducing it. We give characterizations of the enriched structures in terms of first order deformations of the curve, certain line bundles on appropriate subcurves and cohomology groups of the dual graph. Finally, we construct the moduli space of enriched stable curves as an open subscheme of a blow up of the moduli space of stable curves... |
