I will report on a joint work (in progress) with Hamid Abban, Erroxe Etxabarri-Alberdi, Dongchen Jiao, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Elena Denisova, and Theo Papazachariou about the K-moduli of smooth Fano threefolds in deformation families 2-22, 2-24, 2-25, 3-12, 3-13, 4-13 (see this website for the description of these families). These are all 1-dimensional families of smooth Fano threefolds for which K-moduli exist. We know all smooth K-polystable Fano threefolds in these families. I will explain how to find their K-polystable singular limits.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
