Break divisors and compactified Jacobians

 

Let X be a genus g strictly semistable family of curves over C[[t]]. We show, using break divisors introduced by Mikhalkin and Zharkov, that all degree g Simpson compactified Jacobians of X are identical. As a consequence , we resolve a conjecture of Payne, and show that the unique degree g Simpson compactified Jacobian can be constructed from the break divisor decomposition introduced by An-Baker-Kuperberg-Shokrieh, using Mumford's non-Archimedean uniformization theory.