Math 263: Analytic Techniques in Algebraic Geometry

Tuesday, Thursday 10-11:30am, Science Center 310

Course website:


Tristan Collins
Email: tcollins at math dot harvard dot edu
Office: Science Center 239


The course syllabus is here.

Course References


This is approximate. I will attempt to keep track of all the references used in class.

Date Material Problems/Handouts
Sept. 1-8 Complex and Kahler Manifolds, Sheaf Theory: References: (GH)-Chapter 0, (Sz)-Chapter 1,(P) pages 70-98, (Gun)- Sheaf Theory
Problem Set 1
Sept.12-29 Vanishing Theorems Kodaira, and Kodarai-Akizuki-Nakano Vanishing Theorems, Bochner-Kodaira formulas, (P), (Dem, Ch. VII)
Oct. 3-7 Homander's L2 estimates The case of one complex dimension (Ber). The finite dimensional case.
Oct. 11, 13 Hormander's L2 estimates The case of smooth metrics (Dem, Ch. VII), (Dem1), (Ber).
Oct. 17-21 Multiplier ideal sheaves Pluripotential theory (Dem, Ch. I), singular metrics, Nadel and Kawamata-Viehweg vanishing (Dem1), (Ber).
Oct. 24- 26 Vanishing Theorems, Multiplier Ideals From the Algebraic Side Ch. 9 (Laz2),(Dem),(Dem1) Problem Set 2
Oct. 31-Nov. 15 Ohsawa-Takegoshi, Invariance of Plurigenera (Bl) Section 9, (Pa)
Nov. 17-22 Demailly Regularization and applications (Dem1)
Nov. 29- Dec. 2 Positivity of relative adjoint bundles