Geometry & Topology Seminar: Kähler-Einsten metric, K-stability and moduli of Fano varieties

Abstract: Constructing moduli spaces for algebraic varieties has roots in many different fields, e.g. number theory, complex analysis, mathematical physics etc. It is often related to stability notions. The first framework of the construction is Mumford’s geometric invariant theory (GIT), which provides a successful moduli theory for algebraic curves. For higher dimensional case, one needs to seek for new theory beyond the GIT. For Fano varieties, many examples seemed to suggest to higher dimensional geometers that a good moduli theory did not exist, but in the last decade the picture has been demystified by considering the concept of K-stability.

Host: Xiang Tang