Torelli theorem for stable curves
Algebraic Geometry
2011-07-29 v4
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 the finite fibers. We also bound the dimension of the infinite fibers. In particular, we obtain that the compactified Torelli map is injective away from curve with separating nodes if and only if the genus is at most 4.
Keywords
Cite
@article{arxiv.0904.4039,
title = {Torelli theorem for stable curves},
author = {Lucia Caporaso and Filippo Viviani},
journal= {arXiv preprint arXiv:0904.4039},
year = {2011}
}
Comments
Final version: expository changes in 4.1 and 4.3. To appear on JEMS. 34 pages