|
Lecturer |
Prof. Dr. Peter S. Jossen |
Lectures | Tue 10-12, HG F26.3 |
Coordinator |
Riccardo Ferrario |
Exercises |
Thu 12-13, HG F26.3 |
First lecture: Tuesday, February 23, 2016
First exercise class: Thursday, February 25, 2016
Introduction to the theory of complex abelian varieties. Complex tori and Polarisations, Vector bundles on complex tori, cohomology of line bundles, Theta functions and Riemann's Theta relations, Hodge structures, the Hodge/Mumford-Tate group and the Hodge conjecture.
Basic algebraic and differential geometry will be helpful, but is not strictly necessary.
There will be a weekly exercise sheet, uploaded before the lecture on Tuesday. The exercise class on Thursday is an occasion to discuss and work on the exercises together.
Week 1 |
First exercise sheet on lattices and tori, available here |
Week 2 |
Exercise sheet 2 on differential forms |
Week 3 |
Exercise sheet 3 on theta functions |
Week 4 |
Exercise sheet 4 on line bundles |
Week 5 |
Exercise sheet 5 on Néron-Severi group and the Appell-Humbert theorem |
Week 6 |
Exercise sheet 6 |
Week 7 |
Exercise sheet 7 |
Week 8 |
Exercise sheet 8 on duality of complex tori and Poincarè's reducibility theorem |
Week 9 |
Exercise sheet 9 on endomorphism groups of abelian varieties |
Week 10 |
No new exercise sheet and no exercise class this week |
Week 11 |
Exercise sheet 10 |
Week 12 |
Exercise sheet 11 |
Week 13 |
No exercise class |
Week 14 |
No exercise class |
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