1. Contents

In this course, we are going to give a quick introduction to the theory of algebraic surfaces, for students who might had little experience with algebraic geometry.

(1) divisors and projective embedding

(2) intersection theory

(3) Riemann-Roch theorem

(4) birational maps

(5) surface singularities

(6) minimal models

(7) birational classification

(8) ruled and rational surfaces

(9) elliptic surfaces

(10) surfaces with Kodaira dimension 0

(11) K3 surfaces

(12) surfaces of general type

(13) geography of surfaces of general type

(14) some moduli spaces

2. Course prerequisite：

Undergraduate algebra, some commutative algebra, some basic algebraic geometry (varieties, sheaf cohomology )

3. Reference material ( textbooks)：

(1) A. Beauville, Complex algebraic surfaces.

(2) W. Barth, C. Peters, A. Van der Ven, Compact complex surfaces.

(3) R. Hartshorne, Algebraic geometry.

(4) M. Reid, Chapters on algebraic surfaces, in Complex Algebraic Geometry. IAS/Park City Math 3.

4. Grading scheme：

(1) Term paper/Oral Presentation 60 %

(2) Homework 40 %

5. Course Credit：2

Course No.: NCTS5064

Course ID: V41 U2080

6. Join us online

https://www.google.com/url?q=https://us02web.zoom.us/j/83802949647?pwd%3DYXGQvLkqvEWiRJyhzkt5jRYRpsojt3.1&sa=D&source=calendar&ust=1787386194208053&usg=AOvVaw175szeVLGQkdbK0ZsvCs2e