Fall 2005

Introduction to Algebraic Geometry

代數幾何導論

Course Information

Instructor : Jungkai Chen陳榮凱

Place: Math Bldg ?

Hours: Fri. 2,3,4

First meeting: Sep 23. 2005.

Contents：

This course is intended to introduce the modern language in algebraic geometry. Classically, the main objects in algebraic geometry are algebraic varieties. However, it turns out that it’s more convenient to consider the setting of schemes which involve richer structure. The following is the plan:

1. Varieties (affine and projective)

2. Why scheme?

3. Sheaves

4. Definition of schemes

5. Properties of schemes

6. Divisors

7. Projective morphisms

8. Differentials

9. Formal scheme

10. Sheaf cohomology

11. Cohomology of projective spaces

12. Serre duality

Course prerequisite：

Algebra is required. Some experience in commutative algebra is preferred..

Reference material ( textbook(s) )：

1. R. Hartshorne: Algebaic Geoemtry, Graduate Text in Mathematics 52, Springer Verlag

2. D. Eisenbud; J. Harris: The Geometry of Schemes, Graduate Text in Mathematics, Springer Verlag

Grading scheme：

Homework 50%

Presentation 30%

Participation 20%