曲线的高次对称积的 Torelli 定理
代数几何
2021-09-28 v2
摘要
我们证明:除非 g=2,否则具有同构对称积的两个亏格为 g 的光滑射影曲线 C_1 与 C_2 是同构的。这推广了 Martens 的定理。
关键词
引用
@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}
}
备注
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