Complex Algebraic Surfaces: TCC course

Cubic surface


14:00 to 16:00 Thursdays. First lecture: 02/05/19. No lecture on 13/06/19 and 20/06/19

Replacement lectures on Monday 13/05/19 from 14:00 to 16:00.


Enriques' classification of complex algebraic surfaces is a beautiful piece of classical algebraic geometry. We will begin by introducing the theory of algebraic surfaces; reviewing intersection theory on surfaces, the Riemann-Roch theorem and Picard group. We then move toward understanding the classification, via a number of landmark results. We then give a survey of the principal classes of surfaces which appear in the classification.

We will assume some familiarity with the basic notions in algebraic geometry; although the Picard group, amplitude, and intersection multiplicity of curves will all be covered (though quite briefly). A basic familiarity with complex manifolds will be assumed. Some tolerance for the language of schemes has advantages, but is not required.

Lecture Notes

Notes will be added here throughout the course.


Main references for the course. General Algebraic Geometry references Additional references:


If you require assessment for this class please contact me for recommended essay titles.