A compactification of the universal Picard variety over the moduli space of stable curves

A Compactification of the Universal Picard Variety over the Moduli Space of Stable Curves

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A COMPACfIFICATION OF mE UNIVERSAL PICARD VARIETY OVER mE MODULI SPACE OF STABLE CURVES

0.1. Statement of the problem. In this paper we construct a geometrically meaningful compactification for the relative degreed Picard variety associated to a family of stable curves. More precisely, let 1/ -+ B be a (proper and flat) family of stable curves of genus g and let f,,/B -+ B be the corresponding family of Jacobians; we want to answer the following question: does there exist a compac...

Compactification of the Universal Picard over the Moduli of Stable Curves

A. This article provides two different, but closely related, moduli problems, which in characteristic zero provide a type of compactification of the universal Picard over the moduli of stable curves. Although neither is of finite type, both are limits of a sequence of stacks, each of which is a separated algebraic stack of finite type. We discuss relations to previous compactifications a...

The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves

We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Graßmannian. It has all the properties asked for by Teixidor.

A Compactification of a Fine Moduli Space of Curves