Algebraic surfaces provide profound concrete examples in algebraic geometry and have deep connection to the theory of 4-manifolds. The main goal is the classification of surfaces by Enrique-Kodaira and understanding the properties of each type in the classification. Please see below for what will be covered for the topic course.

Course notes

- Intersection pairing on Surfaces (notes)
- Riemann-Roch theorem and Nakai-Moishezon criterion (notes)
- Monoidal transformations (notes)
- Birational transformations and minimal models of surfaces (notes)
- Rule surfaces (notes)
- Rational surfaces (notes)
- Castelnuovo's Criterion of Rationality (notes)
- Surfaces with p_g=0, q>0 (notes)
- Surfaces with Kodaira Dimension 0 (notes)
- K3 surfaces and Enrique Surfaces (K3s) (Enriques)
- Surfaces with Kodaira Dimension 1 and Elliptic surfaces (notes)
- More on Elliptic surfaces (notes)
- Surface of general types (notes)
- Rational surfaces with an anti-canonical cycle and its Torelli theorem (notes)

- Algebraic Geometry, R. Hartshorne.
- Complex Algebraic Surfaces, A. Beauville.
- Compact Complex Surfaces, W. Barth, K. Hulek, C. Peters and A. Van de Ven.