Torelli theorem for stable curves

  • Lucia Caporaso

    Università degli studi Roma Tre, Italy
  • Filippo Viviani

    Università degli studi Roma Tre, Italy


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.

Cite this article

Lucia Caporaso, Filippo Viviani, Torelli theorem for stable curves. J. Eur. Math. Soc. 13 (2011), no. 5, pp. 1289–1329

DOI 10.4171/JEMS/281