Torelli theorem for stable curves

Details Torelli theorem for stable curves Torelli theorem for stable curves

2009-04-26

arxiv.org/abs/0904.4039v4

J. Eur. Math. Soc. (JEMS) 13 (2011), no. 5, 1289--1329

Mathematics

Algebraic Geometry

Final version: expository changes in 4.1 and 4.3. To appear on JEMS. 34 pages

Scientific paper

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.

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