Summer term 2017:
Lecture on Moduli spaces, stability conditions, and birational geometry
|News:||No lecture on Friday, 30.06.2017!|
|Time and location:||Friday, 10-12 h, at MPI MiS G3 10, see also here|
|First lecture:||Fri, April 7, 2017|
|Prerequisites:||Undergraduate course in algebraic geometry, e.g. scheme theory, divisors, line bundles, coherent sheaves. Also basic knowledge of (algebraic) topology would be helpful.
If necessary a small repetition of basics from algebraic geometry at the beginning is possible.
|Content of the lecture:||This course introduces students with basic knowledge of algebraic geometry to the theory of moduli spaces of sheaves. While curves and surfaces may often be studied via explicit equations it becomes more and more difficult in higher dimensions to detect interesting geometric properties from equations. Moduli spaces of sheaves (or stable objects) are an important class of examples of higher dimensional algebraic varieties and their geometric properties are studied through the geometry of the objects they parametrize. During the course we will encounter the following topics:
The lecture is easier to follow, more useful, and much more fun if you work through the exercise sheets which you can download here: