Complex Analysis II

Complex Analysis II (Winter 2019)

News

• The next exams are offered at October 8/9 from 12-14 pm. The exams will take place in MA 874/875. For appointments please contact Beate Niessen before September 21. After September 21 no appointments are possible.

Contents

(almost) complex structures, Riemann surfaces, complex vector bundles, Poincare-Hopf index theorem, holomorphic structures, classification of line bundles, Riemann-Roch theorem

Exercise Sheets

• Exercise sheet 01, due October 30
• Exercise sheet 02, due November 08
• Exercise sheet 03, due November 15
• Exercise sheet 04, due November 22
• Exercise sheet 05, due November 29
• Exercise sheet 06, due December 06
• Exercise sheet 07, due December 13
• Exercise sheet 08, due December 20
• Exercise sheet 09, due January 10
• Exercise sheet 10, due January 17
• Exercise sheet 11, due January 24
• Exercise sheet 12, due January 31

Homework policy

• To get a certificate for the tutorial you need to obtain an average grade of 50% on the homework assignments.

Literature

There are lecture notes:

• Riemann Surfaces

Here are some other lecture notes and recommendations:

• Franz Pedit, C-seminar, Lecture Notes
• Oliver Knill, A short introduction to several complex variables, 1996
• S. Donaldson, Riemann Surfaces, Oxford graduate texts in Mathematics 22, 2011. Here is an older version as pdf
• Alexander I. Bobenko, Lecture Notes
• For the first part of the course. Here are lecture notes from Differential geometry II. Ulrich. Pinkall, Analysis and geometry on manifolds
• Werner Ballmann, Lectures on Kähler manifolds, ESI Lectures in Mathematics and Physics, European Mathematical Society, 2006