Torelli's theorem for high degree symmetric products of curves
Algebraic Geometry
2021-09-28 v2
Abstract
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.
Cite
@article{arxiv.math/0208180,
title = {Torelli's theorem for high degree symmetric products of curves},
author = {Najmuddin Fakhruddin},
journal= {arXiv preprint arXiv:math/0208180},
year = {2021}
}
Comments
D. Huybrechts has pointed out an error in the proof when g = 2. Also, we were recently informed that the result in the case g > 2 was proved earlier by Ciliberto and Miranda in "On the symmetric products of a curve", Arch. Math. (61), 285-290, 1993