K-stability of cubic fourfolds
Algebraic Geometry
2022-01-11 v2 Differential Geometry
Abstract
We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the corresponding GIT stabilities, which was studied in detail by Laza. In particular, this implies that all smooth cubic fourfolds admit K\"ahler-Einstein metrics. Key ingredients are local volume estimates in dimension three due to Liu-Xu, and Ambro-Kawamata's non-vanishing theorem for Fano fourfolds.
Keywords
Cite
@article{arxiv.2007.14320,
title = {K-stability of cubic fourfolds},
author = {Yuchen Liu},
journal= {arXiv preprint arXiv:2007.14320},
year = {2022}
}
Comments
21 pages. Comments welcome. v2: exposition improved, to appear in J. Reine Angew. Math. (Crelle's Journal)