Math 263: Analytic Techniques in Algebraic geometry

Math 263: Analytic Techniques in Algebraic Geometry

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

Course website: math.harvard.edu/~tcollins/Math263.html

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

The course syllabus is here.

(GH) Griffiths-Harris: Principles of Algebraic Geometry
(Sz) Székelyhidi: Introduction to Extremal metrics (PDF)
(P) Phong: Course on Complex Analysis and Riemann Surfaces (notes by Qi You) (PDF)
(Gun) Gunning: Lectures on Riemann Surfaces
(Dem) Demailly: Complex analytic and differential geometry (PDF)
(Dem1) Demailly: Anaytic methods in algebraic geometry (PDF)
(Ber) Berndtsson: L2 methods for the dbar equation (PDF)
(Laz) Lazarsfeld: Positivity in Algebraic Geometry 1 and 2
(Bl) Blocki: Several Complex Variables ( PDF )
(Pa) Paun: Siu's invariance of plurigenera: A One-Tower proof ( PDF )

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