Corpus ID: 15844857

# Torelli's theorem for high degree symmetric products of curves

@article{Fakhruddin2002TorellisTF,
title={Torelli's theorem for high degree symmetric products of curves},
author={Najmuddin Fakhruddin},
journal={arXiv: Algebraic Geometry},
year={2002}
}
• N. Fakhruddin
• Published 23 August 2002
• Mathematics
• arXiv: Algebraic Geometry
We show that two smooth projective curves C_1 and C_2 of genus g which have isomorphic symmetric products are isomorphic unless g=2. This extends a theorem of Martens.
6 Citations
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#### References

SHOWING 1-6 OF 6 REFERENCES
Duality between $D(X)$ and $D(\hat X)$ with its application to Picard sheaves
f(a) = ί f(v)e>>dv Jv gives an isometry between L\V) and L(V), where V is the dual vector space of V and < , >: Vx V -> R is the canonical pairing. In this article, we shall show that an analogyExpand