K-stability of cubic fourfolds

Recently there has been tremendous progress on constructing (projective) moduli spaces of Fano varieties using K-stability. In this talk, we will show that the K-moduli space of cubic fourfolds coincide with their GIT moduli space. In particular, all smooth cubic fourfolds are K-stable as well as those with simple singularities. The key ingredients are local volume estimates in dimension 3 due to Liu-Xu, Ambro-Kawamata non-vanishing theorem for Fano 4-folds, and degeneration of K3 surfaces.

Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09