Classification of vector bundles over the Riemann Sphere [Geometry]

Javier Alcaide (Mestrado em Matemática - FCUL)

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.

Room 6.2.33 [⤴]Fundação para a Ciência e Tecnologia