K-stability of Fano varieties via admissible flags
Algebraic Geometry
2022-06-15 v3 Differential Geometry
Abstract
We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of K\"ahler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) to compute the stability thresholds for hypersurfaces at generalized Eckardt points and for cubic surfaces at all points, and (c) to provide a new algebraic proof of Tian's criterion for K-stability, amongst other applications.
Keywords
Cite
@article{arxiv.2003.13788,
title = {K-stability of Fano varieties via admissible flags},
author = {Hamid Abban and Ziquan Zhuang},
journal= {arXiv preprint arXiv:2003.13788},
year = {2022}
}
Comments
v2: several arguments have been strengthened, most notably many K-stability results are improved to uniform K-stability. v3: minor revision. To appear in Forum Math. Pi