凯勒几何中能量泛函的一致K-稳定性与渐近性
微分几何
2020-05-21 v5 代数几何
摘要
考虑一个极化的复流形(X,L)以及由(X,L)的检验构型上的正度量所定义的L上的一束正度量射线。对于凯勒几何中大多数常见泛函，我们证明了沿该射线的无穷远处斜率由在检验构型定义的L上的非阿基米德度量处计算该泛函的非阿基米德版本（如我们早期论文中所定义）给出。利用这一渐近结果，我们证明Mabuchi泛函的强制性蕴含一致K-稳定性。
引用
@article{arxiv.1603.01026,
title = {Uniform K-stability and asymptotics of energy functionals in K\"ahler geometry},
author = {Sébastien Boucksom and Tomoyuki Hisamoto and Mattias Jonsson},
journal= {arXiv preprint arXiv:1603.01026},
year = {2020}
}
备注
New version with errata (an error was found in the proof of Theorem 5.6). The affected parts of the paper are marked in red