Por Javier Alcaide (Mestrado em Matemática da FCUL).

Abstract: We will give a brief introduction to the theory of compact Riemann surfaces, as an approach to algebraic geometry. Objects like sheaves and vector bundles play an important role in this subject, as they allow us to understand global properties of a surface looking only at local information. After giving some important results of sheaf cohomology, like Serre's duality or the Riemann-Roch theorem, we will use these tools to classify holomorphic vector bundles over the Riemann sphere.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.