4 hours of lectures and exercises per week.
Lecturer: Jesper Funch Thomsen Content: An algebraic space is the zero set of a collection of polynomial functions. In this course we will give a detailed description of such spaces. We will discuss how to equip algebraic spaces with a topology called the Zariski topology, and see how this topology can be used to give a satisfactory definition of dimension of an algebraic space. Other subjects to be discussed include: morphisms between algebraic spaces, products of algebraic spaces, sheaves, algebraic varieties and projective varieties. Algebraic geometry is a mixture of pure algebra and geometry. It gives us a dictionary of how to translate algebraic results into geometric results and vice versa. The main goal of this course is to describe this beautiful connection.
Prerequisites: Algebra 2. Literature: D. Mumford: "The red book of varieties and scemes" Springer Verlag