A Generalized Torelli Theorem

Details A Generalized Torelli Theorem A Generalized Torelli Theorem

2000-01-26

arxiv.org/abs/math/0001152v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

Given a smooth projective curve $C$ of genus $g$ over the complex numbers,
Torelli's thoerem asserts that the pair $(J(C),W^{g-1})$ determines $C$, where
$W^{g-1}$ is an image of the $g-1$st symmetric power of $C$ inside the Jacobian
under an Abel-Jacobi map. We show that the theorem holds with $g-1$ replaced by
an integer $d$ in the range $1\le d\le g-1$.

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