Filippo Viviani: On the classification of fine compactified Jacobians of nodal curves
Abstract: We study the problem of characterizing fine compactified Jacobians of nodal curves that can arise as limits of Jacobians of smooth curves. The answer is given in terms of a new class of fine compactified Jacobians, that we call fine V-compactified Jacobians, and that is strictly larger than the class of fine classical compactified Jacobians, as constructed by Oda-Seshadri, Simpson, Caporaso and Esteves. We give several characterizations of fine V-compactified Jacobians. Furthermore, we show that most of the known properties of fine classical compactified Jacobians extend to fine V-compactified Jacobians: the relation to the Neron models of Jacobians, the autoduality property, the Fourier-Mukai equivalences, the perverse filtration of their cohomology, the relation to Mumford models of Jacobians.
