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 %