# SoSe 16 - Complex Analysis III

## Complex Analysis III - Complex Geometry

### Dates

Monday, 10 - 12 h in WSC-S-U-3.03

Wednesday, 14 - 16 h in WSC-N-U-4.04

### Exercise session

Thursday, 10 - 12 h in WSC-S-U-3.02 (Dr. Tim Kirschner)

During the exercise session we will discuss and work on problems that are posted on Friday afternoon.

### Moodle

The course's moodle pages can be found here. The password necessary to enroll online was provided during the first lecture and can also be obtained by sending an eMail to Daniel Greb or Tim Kirschner.

### Contents

In this course we will study complex manifolds and their analytic subsets, based on the basic results presented in Complex Analysis II - Complex Manifolds.

### Topics

- local structure of analytic sets and their singularities
- extension of analytic sets (Remmert-Stein Theorem)
- divisors and line bundles
- submanifolds of projective spaces, Chow's Theorem
- cohomology, exact sequences
- finiteness of cohomology and its consequences for the geometry of Riemann surfaces

### Literature

- Fritzsche, Grauert: From holomorphic functions to complex manifolds, Springer
- Gunning: Introduction to Holomorphic Functions of Several Variables, Wadsworth & Brooks/Cole
- Huybrechts: Complex Geometry, Springer
- Kaup,Kaup: Holomorphic functions of several variables, de Gruyter
- Range: Holomorphic Functions and Integral Representations in Several Complex Variables, Springer