1. Introduction & Purposes

Abelian varieties are one of important topics in algebraic geometry and number theory. There are many deep and interesting results established and also many problems remain to be investigated. This short course aims at graduate students and advanced undergraduate students, and its goal is to introduce abelian varieties through the analytic theory.

The present course serves as the first episode of the coming Fall course “Moduli spaces of abelian varieties and Hecke symmetry” by Prof. Ching-Li Chai. 

 

2. Outline & Descriptions

Complex tori, line bundles, classification of line bundles on complex tori, cohomological groups of complex tori and abelian varieties, ample and very ample line bundles and projective morphism, dual abelian varieties, the Riemann-Lefschetz theorem.

 

References:

[1] David Mumford, Abelian varieties.

[2] Olivier Debarre, Complex tori and abelian varieties.

 

3. Registration

https://forms.gle/zKuenYuPYFCe6th1A