We cover the basic theory of
compact Riemann surfaces, following the book of Forster. Along the way
we introduce the basic theory of sheaves and the related cohomology
theory. This is a crucial preparation for the Riemann-Roch theorem and
Serre Duality. We shall also treat algebraic functions in this context
and introduce the associated branched covers.
In mathematical physics the covering spaces related to algebraic functions appear in analytic perturbation theory, although classical texts do not explain well the relation to modern Riemann surface theory. I hope to clarify this for the participants in this course.
- Kursleiter:in: Prof. Dr. Markus Klein