Prerequisites
Algebraic Geometry 1 (the notion of varieties and how to work with them); Algebraic Geometry 2 (schemes, coherent sheaves; we will use cohomology of sheaves and the basics will be recalled); Algebraic Topology (homology and cohomology groups); Complex Analysis (holomorphic functions). The knowledge of Riemann surfaces is also preferred.
Aim of the course
Abelian varieties are smooth projective varieties with a group structure. They are very important in algebraic geometry and number theory. In this course, the students will apply their knowledge and skills of algebraic geometry to the study of abelian varieties. We will go through the basic theory of abelian varieties from both analytic and algebraic point of views. We will cover the topics such as cohomology of line bundles, the dual abelian variety, polarization, isogenies, etc. By the end, the students are expected to have the required knowledge so that they feel comfortable working with such objects.
Lecturers
Mingmin Shen (UvA) and Eugenia Rosu (Leiden)
- Docent: Eugenia Rosu
- Docent: Mingmin Shen