Prof. Dr. Mark Hamilton

Lecture: Riemann surfaces

Riemann surfaces are complex 1-dimensional manifolds. They are the simplest non-trivial objects of complex algebraic geometry. This lecture is an introduction to the theory of Riemann surfaces.

Some of the topics are: Definitions and basic properties. Constructions of Riemann surfaces and coverings. Sheaves and cohomology. Divisors, the Riemann-Roch Theorem and Serre duality. Differential forms and Abel's Theorem.

• Time and place: Tue, Thu 12-14, HS A 027
• First lecture: April 25, 2017
• Prior knowledge: Complex analysis I. Some background knowledge in algebra, topology or differential geometry is helpful.

Exercises

• Exercise class: Mo 16-18, HS A 027 (Danu Thung)
• First exercise class: May 8, 2017

Exercise sheets

• Exercise sheet 1
• Exercise sheet 2
• Exercise sheet 3
• Exercise sheet 4
• Exercise sheet 5
• Exercise sheet 6
• Exercise sheet 7
• Exercise sheet 8
• Exercise sheet 9
• Exercise sheet 10

Literature

Some references are (further references will be provided during the lecture):

• O. Forster: Lectures on Riemann Surfaces. Springer Verlag
• S. Donaldson: Riemann surfaces. Oxford University Press
• R. C. Gunning: Lectures on Riemann Surfaces. Mathematical Notes. Princeton University Press