ABUNDANCE ON GENERAL COMPLEX MANIFOLDS

Expositor: Gunnar Magnússon
Institución: : Institut Fourier, Université Joseph Fourier, Francia.

Jueves 25 de julio de 2013.
15:00-16:00 hrs.

Resumen: Let X be a compact Kahler manifold of dimension n and let K be its canonical bundle. The abundance conjecture says that the Kodaria dimension of X is equal to the numerical dimension of K If true, this provides an equality algebraic and cohomological objects. In this talk we will produce an example of a non-Kahler manifold on which the abundance conjecture fails. Our example is an echo of earlier ones of Ueno, whose relevance to this conjecture was somewhat overlooked since the abundance conjecture hadn’t been made when they were constructed. We will start by a quick discussion of the abundance conjecture and its place in complex geometry. Next we will review a few details of the geometry of Kahler manifolds with trivial canonical bundle, then construct the examples themselves and prove they have the required properties.