Topics in Algebraic Geometry, I

代數幾何專題 I

Course Information

Instructor : Jungkai Chen陳榮凱

Place and Hours: Tu 5.6. N504 新生504 / Tu 7 N502新生502

 

 

 

Syllabus

The two main theme of this course is minimal model theory.

There are some important recent developments in the theory of minimal model using the technique of multiplier ideals and Shokurov’s work. In order to introduce these developments, we would like to review previous work on minimal model theory in dimension three in this course.

 

Notes:

        Chapter 1. Preliminary

        Chapter 2. Algebraic Surfaces

        Chapter 3. Three Dimensional Terminal Singularities

        Chapter 4. Explicit Minimal Model Program in Dimension Three

 

Topics:

        Sep. 16    Overview of Minimal Model Program, divisors

        Sep. 23    Riemann-Roch Theorem

                        Algebraic Varieties

        Sep. 30    Intersection Theory and Riemann-Roch Theorem on Surfaces

        Oct. 7      Castelnuovo’s Contraction Theorem,

Minimal Model Program for Surfaces

        Oct. 14    Cone Theorem, Contraction Theorem

Canonical Singularities

 

Prerequisite

Any ambitious student is welcome.

 

Reference:

Kollar, Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math 134. 1998.

Matsuki, Introduction to Mori Program, Springer, 2001.

Reid, Young person’s guide to canonical singularities. Proc. Symp. Pure Math 46, 1985

 

Grading:

        Participation     30 %

        Term Paper      70 %