Torelli theorem for stable curves

Lucia Caporaso; Filippo Viviani

Journal of the European Mathematical Society (2011)

  • Volume: 013, Issue: 5, page 1289-1329
  • ISSN: 1435-9855

Abstract

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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.

How to cite

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Caporaso, Lucia, and Viviani, Filippo. "Torelli theorem for stable curves." Journal of the European Mathematical Society 013.5 (2011): 1289-1329. <http://eudml.org/doc/277799>.

@article{Caporaso2011,
abstract = {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.},
author = {Caporaso, Lucia, Viviani, Filippo},
journal = {Journal of the European Mathematical Society},
keywords = {Torelli map; Jacobian variety; theta divisor; stable curve; stable semi-abelic pair; compactified Picard scheme; semiabelian variety; moduli space; dual graph; Torelli map; Jacobian variety; theta divisor; stable curve; stable semi-abelic pair; compactified Picard scheme; semiabelian variety; moduli space; dual graph},
language = {eng},
number = {5},
pages = {1289-1329},
publisher = {European Mathematical Society Publishing House},
title = {Torelli theorem for stable curves},
url = {http://eudml.org/doc/277799},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Caporaso, Lucia
AU - Viviani, Filippo
TI - Torelli theorem for stable curves
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 5
SP - 1289
EP - 1329
AB - 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.
LA - eng
KW - Torelli map; Jacobian variety; theta divisor; stable curve; stable semi-abelic pair; compactified Picard scheme; semiabelian variety; moduli space; dual graph; Torelli map; Jacobian variety; theta divisor; stable curve; stable semi-abelic pair; compactified Picard scheme; semiabelian variety; moduli space; dual graph
UR - http://eudml.org/doc/277799
ER -

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