Compactifying the Néron Model and Break Divisors

We review Caporaso’s theory of compactified Picard schemes, and how it provides natural and distrinct compactifications of the Néron models of Jacobians of curves. Then, we reframe the combinatorial aspects of the theory in the language of break divisors of tropical curves. We conclude with a discussion on the question of finding a canonical compactification of the Néron model.