Overview
The classical Baily-Borel compactification is yields a canonical compactification of moduli spaces of certain Calabi-Yau varieties including K3 surfaces and abelian varieties. The existence of the Baily-Borel compactification is closely tied to ampleness of the so-called Hodge line bundle on these moduli spaces. Recently, Bakker-Filipazzi-Mauri-Tsimerman constructed Baily-Borel compactifications for moduli of Calabi-Yau varieties beyond the classical case and prove the b-semiampleness conjecture regarding positivity of the Hodge bundle. The goal of this seminar is to study this work, as well as the previous work of Bakker-Brunerbarbe-Tsimerman and Bakker-Klingler-Tsimerman on o-minimality and Hodge theory leading up to BFMT.
Schedule
We generally meet on Fridays from 1:50 pm to 3 pm in 3206 unless otherwise indicated by **.
09/18 Introduction to o-minimal structures (Patrick)
09/23** Overview of b-semiampleness (Dori)
10/09 Definable analytic spaces (Anurag)
10/16-10/23 Definable GAGA and definable images
10/30 Definability of the period map
11/6 Quasi-projectivity of period images
(TBD) Baily-Borel compactifications and b-semiampleness