Related papers: Combinatorics of compactified universal Jacobians

We introduce a general abstract notion of fine compactified Jacobian for nodal curves of arbitrary genus. We focus on genus 1 and prove combinatorial classification results for fine compactified Jacobians in the case of a single nodal curve…

We construct modular compactifications of the universal Jacobian stack over the moduli stack of reduced curves with marked points depending on stability parameters obtained out of fixing a vector bundle on the universal curve. When…

Extending the definition of $V$-stability conditions, given by Viviani in a recent preprint, we introduce the notion of universal stability conditions. Building on results by Pagani and Tommasi, we show that fine compactified universal…

This is the third paper in a series, following [FPVa] and [FPVb]. We classify all modular compactifications of the universal Jacobian over $\overline{\mathcal{M}}_{g,n}$, both as stacks and as their relative good moduli spaces. Our main…

We show that relative compactified Jacobians of one-parameter smoothings of a nodal curve of genus g are Mumford models of the generic fiber. Each such model is given by an admissible polytopal decomposition of the skeleton of the Jacobian.…

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 modular compactification of a disjoint union of the generalized Jacobian…

We characterize stable curves $X$ whose compactified degree-$d$ Jacobian is of N\'eron type. This means the following: for any one-parameter regular smoothing of $X$, the special fiber of the N\'eron model of the Jacobian of the generic…

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 concerning the gerbe structure of the universal Jacobian stack over…

In this paper we describe compactified universal Jacobians, i.e. compactifications of the moduli space of line bundles on smooth curves obtained as moduli spaces of rank 1 torsion-free sheaves on stable curves, using an approach due to…

Using the compactified universal jacobian over the moduli space of stable marked curves, we give an expression in terms of natural classes of the zero section of the compactified universal jacobian the (rational) Chow ring. After extending…

For each universal genus-$g$ polarization $\mu$ of degree $d$, we construct a universal tropical Jacobian $J_{\mu,g}^{trop}$ as a generalized cone complex over the moduli space of stable pointed genus-$g$ tropical curves. We show several…

This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the completed local ring of the compactified Jacobian of a nodal curve…

A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1…

We introduce and study a new class of compactified Jacobians for nodal curves, that we call compactified Jacobians of vine type, or simply V-compactified Jacobians. This class is strictly larger than the class of classical compactified…

This is the first paper of a series of three. Here we give an abstract definition of the relative compactified Jacobian of a family of reduced curves. We prove that, under some mild assumptions on the family of curves, the fibres of the…

We introduce a new class of fine compactified Jacobians for nodal curves, that we call fine compactified Jacobians of vine type, or simply fine V-compactified Jacobians. This class is strictly larger than the class of fine classical…

We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold…

In this paper we give a construction of algebraic (Artin) stacks endowed with a modular map onto the moduli stack of n-pointed stable curves of genus g, for g greater than 2. These stacks are smooth, irreducible and have dimension 4g-3+n,…

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 tropicalization of the universal compactified Jacobian…

This article studies the mixed Hodge structures that appear on the complements of generalized theta divisors inside generalized Jacobians of curves with modulus. For a smooth or nodal curve with an effective modulus, the generalized…