  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 compactified Jacobians, as constructed by Oda-Seshadri, Simpson,
Caporaso and Esteves. Inspired by a recent preprint of Pagani-Tommasi, we
characterize fine V-compactified Jacobians as the fine compactified Jacobians
that can arise as limits of Jacobians of smooth curves under a one-parameter
smoothing of the nodal curve or in its semiuniversal deformation space.
Furthermore, fine V-compactified Jacobians are exactly the ones that gives a
compactification of the N\'eron model of the Jacobian of the generic fiber of a
one-parameter regular smoothing of the nodal curve. Finally, we give a
combinatorial characterization of fine V-compactified Jacobians in terms of
their poset of orbits for the action of the generalized Jacobian.
