Algebraic Curves

代數曲線

Course Information:

Instructor : Jungkai Chen陳榮凱

Place: New Math Bldg 103

Hours: Fri..9:10-12:10

Webpage: http://www.math.ntu.edu.tw/~jkchen

First Meeting: 2005, Feb. 25 (Tue.)

Course description:

The purpose of this course is to serve as an introduction to algebraic geometry. We will work on classical theory of curves from the viewpoint of modern algebraic geometry.

Another important topic is the moduli of curves. Roughly speaking, it is a parameter space for curves. There are lots of geometry of curves, such as deformation and curve-counting, can be formulated in terms of geometry of moduli spaces. We will give an introduction to this account.

Topics:

1. affine and projective varieties

2. local properties of plane curves

3. projective plane curves

4. morphisms and rational maps

5. resolution of singularities

6. special divisors on curves

7. families of curves

8. introduction to moduli spaces of curves

Prerequisite: Algebra.

Reference:

Fulton, Algebraic Curves, an introduction to algebraic geometry. Addison Wiley

Harris, Morrison, Moduli of curves, GTM 187, Springer Verlag

Arbarello, Cornalba, Griffiths, Harris, Geometry of algebraic curves, Springer.

Grading:

Homework 50%

Termpaper 50%