Fano 簇的 K-半稳定性开集性
代数几何
2021-11-02 v3 微分几何
摘要
本文中,我们通过证明稳定性阈值是纤维上的可构造函数,证明了 log Fano 对族中 K-半稳定性的开集性。我们还证明任意特殊检验构型源于有界补的 log canonical 位,并建立了稳定性阈值任意极小化子的性质。
引用
@article{arxiv.1907.02408,
title = {Openness of K-semistability for Fano varieties},
author = {Harold Blum and Yuchen Liu and Chenyang Xu},
journal= {arXiv preprint arXiv:1907.02408},
year = {2021}
}
备注
37 pages. Comments are very welcome. v3: to appear in Duke Math. J.. v2: added Theorem 4.5 showing openness of K-stability and constructibility of K-polystability