Affiliation:
1. Department of Mathematics , Northwestern University , Evanston , IL 60208 , USA
Abstract
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.
Funder
National Science Foundation
Subject
Applied Mathematics,General Mathematics
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