To every singular reduced projective curve $ X $ one can associate many fine compactified
Jacobians, depending on the choice of a polarization on $ X $, each of which yields a …

In this article we provide a stack-theoretic framework to study the universal tropical Jacobian
over the moduli space of tropical curves. We develop two approaches to the process of …

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 …

To every singular reduced projective curve X one can associate, following Esteves, many
fine compactified Jacobians, depending on the choice of a polarization on X, each of which …

This paper studies the local geometry of compactified Jacobians. The main result is a
presentation of the completed local ring of the compactified Jacobian of a nodal curve as an …

We study the cohomology of Jacobians and Hilbert schemes of points on reduced and
locally planar curves, which are however allowed to be singular and reducible. We show …

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL
n over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs …

To every reduced (projective) curve X with planar singularities one can associate, following
E Esteves, many fine compactified Jacobians, depending on the choice of a polarization on …

We introduce the abstract notion of a smoothable fine compactified Jacobian of a nodal
curve, and of a family of nodal curves whose general element is smooth. Then we introduce …

The Jacobian varieties of smooth curves fit together to form a family, the universal Jacobian,
over the moduli space of smooth pointed curves, and the theta divisors of these curves form …