Combinatorial Algebraic Geometry: Compactifications of Jacobians of Nodal Curves

Jacobians of smooth curves are well-studied classical objects which have been studied since the work of Riemann. In the time since then, there have been many generalizations of this theory, including in particular constructions of Jacobians for curves with nodal singularities. These Jacobians are typically not projective and, as such, much work has been invested to compactify these objects. In this talk we study a family of compactifications of Jacobians of nodal curves due to Oda and Seshadri. These constructions rely on combinatorial and convex-geometric machinery which is interesting in its own right. Here, we survey both the algebro-geometric and the convex-geometric constructions needed to appreciate Oda-Seshadri's results.