K-stability of cubic fourfolds

Yuchen Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 and Xu, and Ambro-Kawamata's non-vanishing theorem for Fano fourfolds.

Original languageEnglish (US)
JournalJournal fur die Reine und Angewandte Mathematik
DOIs
StateAccepted/In press - 2022

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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