Completions of Period Maps

The course teaches how to describe completions/extensions of period maps, leading to compact Moishezon varieties. It covers constructing completions of period mappings and their application in studying moduli. The key skills taught include understanding the global structure of period maps at infinity, utilizing period matrix representations, and applying Grauert’s result on holomorphic equivalence relations. The teaching method involves theoretical explanations and technical insights. The course is intended for individuals interested in advanced topics in algebraic geometry and Hodge theory.