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arXiv · 2007.14320

K-stability of cubic fourfolds

Yuchen Liu
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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 Kähler-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.

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BibTeXRIS

Yuchen Liu. 2022-01-10. K-stability of cubic fourfolds. https://arxiv.org/abs/2007.14320

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