MA 821 Complex Algebraic Surfaces (Fall 2020)

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

  1. Intersection pairing on Surfaces (notes)
  2. Riemann-Roch theorem and Nakai-Moishezon criterion (notes)
  3. Monoidal transformations (notes)
  4. Birational transformations and minimal models of surfaces (notes)
  5. Rule surfaces (notes)
  6. Rational surfaces (notes)
  7. Castelnuovo's Criterion of Rationality (notes)
  8. Surfaces with p_g=0, q>0 (notes)
  9. Surfaces with Kodaira Dimension 0 (notes)
  10. K3 surfaces and Enrique Surfaces (K3s) (Enriques)
  11. Surfaces with Kodaira Dimension 1 and Elliptic surfaces (notes)
  12. More on Elliptic surfaces (notes)
  13. Surface of general types (notes)
  14. Rational surfaces with an anti-canonical cycle and its Torelli theorem (notes)
  1. Algebraic Geometry, R. Hartshorne.
  2. Complex Algebraic Surfaces, A. Beauville.
  3. Compact Complex Surfaces, W. Barth, K. Hulek, C. Peters and A. Van de Ven.