Lecture Algebraic Surfaces

Lecturer Prof. Dr. Christian Liedtke
Example classes Prof. Dr. Christian Liedtke

Time and place


Mondays, 12:15 - 13:45 in MI 03.10.011

Tuesdays, 10:15 -  11:45 in MI 03.10.011

Example classes will be decided in the first week of the semester


This is a lecture on algebraic geometry introducing the theory of algebraic surfaces. We will start with recalling some basic facts on algebraic curves and their classification. Then, we will turn to algebraic surfaces and their classification: 

  • birational geometry of surfaces, Castelnuovo's contraction theorem, minimal models
  • surface singularities: rational singularities and rational double points
  • Kodaira dimension and the Enriques classification

Then, we will turn to special classes of algebraic surfaces

  • rational surfaces and del Pezzo surfaces
  • elliptic surfaces
  • K3 surfaces and Enriques surfaces
  • surfaces of general type

If time permits, we will discuss arithmetic aspects and we will have a glimpse on the classification of varieties in dimension three.


  • L. Badescu: Algebraic Surfaces
  • A. Beauville: Complex Algebraic Surfaces
  • R. Hartshorne: Algebraic Geometry


A basic knowledge of algebraic geometry.