Products of K-moduli Spaces in Algebraic Geometry

Explore K-moduli spaces and their products in this mathematical seminar lecture where Dr. Theodoros Stylianos Papazachariou from the University of Cambridge delves into the construction and study of moduli spaces of Fano varieties and log Fano pairs. Learn about recent advances in K-stability and its role in constructing these moduli spaces, with particular focus on the local and global structures of K-moduli spaces of product Fano varieties. Discover how connected components containing products must exclusively contain product Fano varieties, and understand the morphism between product K-moduli stacks and their relationship to K-moduli stacks of products. Examine specific examples of reduced connected components of K-moduli stacks of Fano threefolds and log Fano pairs through detailed mathematical analysis.