On quasi-projectivity of the moduli space of good minimal model with $\kappa=1$

Speaker's Name: Masafumi Hattori
Speaker's Affiliation: Nottingham
Speaker's Research Theme(s): Pure Mathematics
Abstract:
Odaka proposed the K-moduli conjecture in 2010, predicting the existence of a moduli space of K-polystable objects with an ample CM line bundle. While this conjecture has been solved in the Fano case, it remains open in general. On the other hand, good minimal models of Kodaira dimension one with only Kawamata log terminal singularities are important objects in algebraic geometry. Furthermore, they are known to be K-stable for suitable choices of polarizations. In this talk, I would like to explain how to show the positivity of the CM line bundle on the normalization of the K-moduli space parameterizing such good minimal models. This talk is partially based on joint work with Kenta Hashizume.

Venue: Maths A17