Lecturer: Johan Dupont and Christina Tønnesen-Friedman
Content:
A complex manifold is a differentiable manifold with a holomorphic structure which means that the notion of holomorphic or complex analytic functions makes sense in this setting. We shall study the basic properties of these manifolds thus generalizing the classical theorems about meromorphic functions on Riemann surfaces (i.e. complex manifolds of dimension 1). The course is of particular interest for students with prior knowledge on Riemann surfaces or algebraic varieties, although this is not a required prerequisite.
Topics are: Complex manifolds and holomorphic vector bundles, Dolbeault cohomology and Hodge theory, Kä hler manifolds and the Hodge decomposition, line bundles and divisors, the Kodaira embedding theorem.
Possible continuation: Moduli spaces of holomorphic vector bundles on Riemann surfaces.
Prerequisites: Kompleks funktionsteori and Topology 1
Literature: Notes by Jørgen Ellegaard Andersen.