On K-moduli of V22

Location: 11th Floor Lecture Hall Speaker Yuchen Liu, Northwestern University Session Chair Philip Engel, University of Illinois, Chicago Abstract V22 is the class of prime Fano threefolds of genus twelve which was discovered by Iskovskikh and studied by Mukai and many others. Despite remarkable progress on the theory of K-stability, we still do not know the K-stability of smooth V22 and their K-moduli space. In this talk, I'll explain that the K-moduli of V22 in codimension 1 parameterizes V22 with at most one nodal singularity. The proof is a combination of deformation theory, K3 surfaces, and K-stability techniques. Based on joint work with Anne-Sophie Kaloghiros, Andrea Petracci, and Junyan Zhao.