Por Ana Margarida Melo (Univ. de Roma e Univ. de Coimbra).
Abstract: Given a reduced (but possibly reducible) curve with locally planar singularities, one can consider several possible compactifications of its Jacobian, depending on a stability condition. The geometry of these objects is very rich and they satisfy a number of properties which are well known for smooth curves, as e.g. autoduality statements. Some of these compactifications glue over the moduli space of stable curves, and they can be used to describe geometrical loci of the moduli space of stable curves itself. In the talk, I will describe a number of different universal compactifications of the Jacobian, describing some of their properties and how they relate with different constructions. I will then indicate a number of possible applications of the subject, possibly mentioning how could some of them be attacked from the point of view of tropical geometry.