Del Pezzo surfaces

Abstract

Del Pezzo surfaces, named after the Italian mathematician Pasquale Del Pezzo, are a central object of study in algebraic geometry. These surfaces exhibit rich geometric properties and have numerous applications in various areas of mathematics, including complex geometry and theoretical physics. In this project, we will explore three different definitions of Del Pezzo surfaces, analyze their equivalences and differences, and delve into some of their geometric properties. We start this project by introducing concepts that will be needed to work and understand the different definitons. And so forth the first two chapters are presented as a continuation of the Algebraic Geometry course in the Advanced Mathematics Master, UB. It is not until the third chapter that the first properties of Del Pezzo surfaces are presented. The foruth and final chapter is based on using the results previously found to give a geometrical structure of some Del Pezzo surfaces.