更高维Fano流形零次循环的无界性
代数几何
2025-12-02 v1 数论
摘要
我们证明了，与del Pezzo曲面不同，更高维Fano流形 generally does not satisfy boundedness properties for their group of -cycles。例如，对于具有奇数度数点的四次三维流形，没有“Coray类型”的上界限制其奇数度数点的最小度数。此外，Fano超曲面的群可以是“无界的”（这与Mumford的无限维性相关），meaning that there is no integer such that -cycles of degree at least are effective。
引用
@article{arxiv.2511.23080,
title = {Unboundedness of zero-cycles on higher dimensional Fano manifolds},
author = {Claire Voisin},
journal= {arXiv preprint arXiv:2511.23080},
year = {2025}
}