Complex Algebraic Geometry Reading Seminar

I organize a reading seminar on the Kähler minimal model program and analytic methods in birational geometry. The topics covered so far:

Spring and Summer 2025

1. 2025.02.26 — Höring–Peternell’s proof of Mori bend and break for Kähler threefolds; Douady spaces.
2. 2025.03.05 — Höring–Peternell’s proof of the cone theorem for Kähler threefolds; Douady spaces.
3. 2025.03.12 — Höring–Peternell’s proof of small and divisorial contractions for Kähler threefolds; Douady spaces.
4. 2025.03.19 — Das–Hacon’s proof of the existence of divisorial contractions for generalized dlt Kähler threefolds.
5. 2025.03.26 — Das–Hacon’s proof of the existence of divisorial contractions for generalized dlt Kähler threefolds (continued).
6. 2025.04.02 — Das–Hacon’s proof of the existence of small contractions for generalized dlt Kähler threefolds.
7. 2025.04.09 — Das–Hacon’s proof of the existence of small contractions for generalized dlt Kähler threefolds (continued).
8. 2025.05.07 — Cao–Höring’s subadjunction; the Ohsawa–Takegoshi $L^2$ extension theorem.
9. 2025.05.08 — The Clemens–Schmid exact sequence.
10. 2025.05.10 — The Demailly–Hacon–Păun extension theorem.
11. 2025.05.21 — Cao–Höring’s subadjunction (continued).
12. 2025.05.28 — Hacon–Păun’s canonical bundle formula for Kähler varieties; existence of a universal deformation space.
13. 2025.05.29 — Degeneration of the Leray spectral sequence for a smooth projective morphism.
14. 2025.06.05 — Betti moduli spaces.
15. 2025.06.11 — Hacon–Păun’s canonical bundle formula; equivalent characterizations of the existence of a universal deformation space.
16. 2025.06.12 — Perverse sheaves; the variational characterization of harmonic metrics; Donaldson’s theorem; the Hitchin–Simpson theorem.
17. 2025.08.01 — A brief introduction to the André–Oort, Ax–Schanuel and Zilber–Pink conjectures; unlikely intersection theory.
18. 2025.08.03 — The attractor conjecture; the Sheng–Xu–Zuo cyclic cover construction of Dolgachev Calabi–Yau varieties.

Fall 2025

1. 2025.09.19 — Hacon–Popa–Schnell’s proof of the Iitaka conjecture when the base is of maximal Albanese dimension.