Technique de descente et théorèmes d'existence en géométrie algébrique. V. Les schémas de Picard : théorèmes d'existence
We study the Torelli morphism from the moduli space of stable curves to the moduli space of principally polarized stable semi-abelic pairs. We give two characterizations of its fibers, describe its injectivity locus, and give a sharp upper bound on the cardinality of finite fibers. We also bound the dimension of infinite fibers.