# 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

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topCaporaso, 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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