The resolution of the degree-2 Abel-Jacobi map for nodal curves-I

Let be a regular local smoothing of a nodal curve. In this paper, we find a modular description of the Neron maps associated to Abel-Jacobi maps with values in Esteves's fine compactified Jacobian and with source the B-smooth locus of either the double product of over B or the degree-2 Hilbert scheme of the family f. This is the first of a series of two papers dedicated to the construction of a resolution of the degree-2 Abel-Jacobi map for a regular smoothing of a nodal curve.