65-417 Complex Geometry
|Time and place:
||Lecture: Wednesdays 12:15-13:45 in H1 and Fridays 8:30-10:00 in H5
Recitations: every other Friday 8:30-10:00 in H5
The main protagonists in complex geometry are complex manifolds. The subject therefore lies at the intersection of differential geometry, algebraic geometry und complex analysis.
Many results are also frequently used in mathematical physics. In this lecture we will study some local theory (holomorphic functions, differential forms,...), complex manifolds, Kähler manifolds, the Hodge decomposition, sheaves and their cohomology, and more.
Despite its connection to many other subjects, the prerequisites are rather modest. A good knowledge of linear algebra (that is, Lineare Algebra I and II) and calculus (that is, Analysis I-III) is definitely necessary. Familiarity with some basic topology, differential geometry and complex analysis might be helpful, but the relevant statements and results will be recalled in the lecture.
The lecture is suitable for students from the 5th semester on.
- P. Griffiths and J. Harris, "Principles of algebraic geometry", John Wiley & Sons, Inc., New York (1994)
- D. Huybrechts, "Complex geometry: an introduction", Springer, Berlin (2005)
- M. Kashiwara and P. Shapira, "Sheaves on manifolds", Springer, Berlin (1994)
- C. Schnell, "Complex manifolds" lecture notes, available at his homepage.
- C. Voisin, "Hodge theory and complex algebraic geometry I", Cambridge University Press, Cambridge (2002)
Oral exam. Solving the homework assignments is an essential part of the lecture.