1.1. Background David Mumford developed geometric invariant theory (GIT)([30]) as a
means to construct moduli spaces. Mumford used GIT to construct the moduli space of …

We construct the logarithmic and tropical Picard groups of a family of logarithmic curves and
realize the latter as the quotient of the former by the algebraic Jacobian. We show that the …

In this paper we describe compactified universal Jacobians, ie, compactifications of the
moduli space of line bundles on smooth curves obtained as moduli spaces of rank $1 …

We construct the logarithmic and tropical Picard groups of a family of logarithmic curves and
realize the latter as the quotient of the former by the algebraic Jacobian. We show that the …

For each universal genus‐g polarization μ of degree d, we construct a universal tropical
Jacobian J μ, gtrop as a generalized cone complex over the moduli space of stable pointed …

Given a family of nodal curves, a semistable modification of it is another family made up of
curves obtained by inserting chains of rational curves of any given length at certain nodes of …

Let g and n be nonnegative integers and A=(a 0,…, an) a sequence of n+ 1 integers
summing up to d. Let M‾ g, n+ 1 be the moduli space of (n+ 1)-pointed stable curves of …

We compute the Kodaira dimension of the universal Picard variety P d, g parameterizing line
bundles of degree d on curves of genus g under the assumption that (d− g+ 1, 2g− 2)= 1. We …

We determine explicitly the Picard groups of the universal Jacobian stack and of its
compactification over the stack of stable curves. Along the way, we prove some results …

In this paper we describe compactifications of the universal Jacobian stack of line bundles
over smooth curves obtained by considering open substacks of the moduli stack of torsion …