483-1 - Algebraic Geometry

Monday, Wednesday, Friday 2:00pm - 2:50pm, Lunt 101
Course website: www.math.northwestern.edu/~tosatti/ag.html

Instructor:

Valentino Tosatti
Email: tosatti@math.northwestern.edu
Office: Lunt 225

Office hours:

Thursdays 1.00pm - 2.00pm
or by appointment

Course Description:

This course is an introduction to the study of complex manifolds and algebraic varieties. See the syllabus below for more detailed content information.

Prerequisites:

Familiarity with single-variable complex analysis.

Textbook:

We will roughly follow the textbook: Another useful references is

Daily Schedule:

This is a tentative syllabus and it is likely to change as the course progresses.

Date Topics Covered Remarks
Sept. 21, 23, 25 Basic theory of holomorphic functions in several variables
Sept. 28, 30, Oct. 2 Complex manifolds, analytic varieties Homework 1
Due October 9 in class
Solution
Oct. 5, 7, 9 Divisors, differential forms Homework 2
Due October 16 in class
Solution
Oct. 12, 14, 16 Vector bundles and sheaves Homework 3
Due October 23 in class
Solution
Oct. 19, 21, 23 Cohomology of sheaves and line bundles Homework 4
Due October 30 in class
Solution
Oct. 26, 28, 30 Chow's Theorem Homework 5
Due November 6 in class
Solution
Nov. 2, 4, 6 Kähler metrics Homework 6
Due November 13 in class
Solution
Nov. 9, 11, 13 Hodge theory Homework 7
Due November 20 in class
Solution
Nov. 16, 18, 20 Kodaira Vanishing Theorem Homework 8
Due November 30 in class
Solution
Nov. 23, 25 Kodaira Embedding Theorem
Nov. 30, Dec. 2 Applications
Take-home final exam Due at 11am on December 7
by email
tosatti@math.northwestern.edu
or in my mailbox in Lunt