# Complex Manifolds 2

**Time and place**:

Dienstag 10-12 Uhr WSC-S-U-3.03

Donnerstag 8-10 Uhr WSC-S-U-3.03

**Exercise class:** To be determined.

*In cae of important collisians with other classes, please let me know as soon as possible.*

There will be a Moodle page for this class where you can find brief summaries of the lectures, homework assignments, a forum to discuss and ask questions. (Subcribe with: ComplexManifolds2 )

**Aimed at: ** Students in Bachelor/Master Mathematics starting from 6. Semster. Basic knowledge on complex functions in several variables, real manifolds, differential forms and de Rham cohomology will be assumed.

**Content:**

Cohomology of complex manifolds has a particularly rich structure. We will analyze this and see how it helps to understand when a complex manifold can be embeded into projective space and described by algebraic equations. In particular all compact Riemann surfaces turn out to arise from polynomial equations.

This gives rise to many open problems relating analysis and algebra.

**Literature:**

There are many beautiful book son the subject. Some examples are:

D. Huybrechts: Complex Geometry, Springer Verlag

P. Griffiths, J. Harris: Principles of Algebraic Geometry.