The arithmetic-geometric mean and isogenies for curves of higher genus
Théorèmes de Lefschetz pour les lieux de dégénérescence
Torelli theorem for stable curves
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.
Trigonal modular curves