Date & Time:
1/22-25 and 1/28-29, 15:00-17:50

Course background and 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 to be investigated in the theory of abelian varieties. Thus, it is useful to learn abelian varieties more. This short course is for graduate students, and its goal is to introduce abelian varieties through the analytic theory.    

Outline & Speakers:

We will discuss the following topics in details:

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, the Riemann-Lefschetz theorem, GAGA principle and Chow’s lemma, polarizations and dual abelian varieties, construction of abelian varieties: moduli and CM abelian varieties.

Prerequisite: Graduate Algebra, Complex analysis, and notions of complex manifolds, algebraic varieties and sheaf cohomology will be helpful.

References:
[1] David Mumford, Abelian varieties.
[2] Olivier Debarre, Complex tori and abelian varieties.

Location:
Room 609, Astro-Math Building