The Torelli theorem for stable curves 
-- Lucia Caporaso, April 17, 2009

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The classical Torelli theorem states that the Torelli map
(mapping a curve to its Jacobian variety, polarized by the
theta divisor) is an injection from the moduli space of smooth
curves to the moduli space of principally polarized abelian
varieties.  The Torelli map can be naturally extended from
stable curves to semiabelic stable pairs.  This map fails to be
injective; I will precisely describe how the Torelli theorem
generalizes.  This is joint work with Filippo Viviani.