相关论文: Compactified jacobians

We study the theta divisor of the compactified jacobian of a nodal, possibly reducible, curve. We compute its irreducible components and give it a geometric interpretation consistent with the classical Brill-Noether theory of smooth curves.…

We look at the decomposition of the compactified jacobian of a singular curve into components and discuss some examples.

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…

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…

The Jacobian $J$ of a complete, smooth, connected curve $X$ admits a canonical divisor $\Theta$, called the Theta divisor. It is well-known that $\Theta$ is ample and, in fact, $3\Theta$ is very ample. For a general complete, integral curve…

We survey the theory of the compactified Jacobian associated to a singular curve. We focus on describing low genus examples using the Abel map.

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…

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 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 natural relative compactifications for the relative Jacobian over a family $X/S$ of reduced curves. In contrast with all the available compactifications so far, ours admit a universal sheaf, after an etale base change. Our…

We construct a good compactification of the variety of irreducible projective plane curves of degree n with d nodes and no other singularities.

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 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.…

We study Esteves's fine compactified Jacobians for nodal curves. We give a proof of the fact that, for a one-parameter regular local smoothing of a nodal curve $X$, the relative smooth locus of a relative fine compactified Jacobian is…

We use orientations on stable graphs to express the combinatorial structure of the compactified universal Jacobians in degrees g-1 and g over the moduli space of stable curves, \Mgb, and construct for them graded stratifications compatible…

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 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 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…

This is an expository paper about the topics listed in the title.

For any positive integer $k$, let $X_k$ be a projective irreducible nodal curve with $k$ nodes. We show that the Betti numbers and the mixed Hodge numbers of the compactified Jacobian $\overline{J_{k}}$ of an irreducible nodal curve $X_k$…