Prof. D. Kotschick and Dr. J. Stelzig: Selected Topics in Complex Geometry

• Time and Place: Mon 12-14, Wed 14-16 room B 047
  
• Exercise class: Wed 16-18, room B 004
  
• Content: This course is about the differences and the similarities between Kähler and projective complex manifolds. A compact complex manifold is called projective if it admits a holomorphic embedding into some complex projective space. It is called Kähler if it admits a hermitian metric with closed fundamental 2-form. Every projective manifold is Kähler but not the other way round. We will begin with the Kodaira embedding theorem, and then go on to study topological and analytic properties that hold for projective manifolds but not necessarily for Kähler ones. The main tools for this come from Hodge theory. Along the way we will also learn more about some facinating open conjectures and problems (e.g. the Hodge conjecture).
  
• for: Master mathematics (or physics) and TMP
  
• Prerequisites: Some previous exposure to either complex or algebraic geometry.
  
• References:
  D. Huybrechts: Complex Geometry, Springer Verlag 2005,
  C. Voisin: Hodge Theory and Complex Algebraic Geometry, I and II, Cambridge University Press 2002.
  
  
• Homework sheets:
  Sheet 1 Sheet 2 Sheet 3 Sheet 4 Sheet 5 Sheet 6 Sheet 7 Sheet 8 Sheet 9 Sheet 10 Sheet 11