Department of Mathematics

Complex Abelian Varieties

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Lecturer Prof. Dr. Peter S. Jossen
Lectures Tue 10-12, HG F26.3
Coordinator Riccardo Ferrario
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.

Exercise sheets and exercise classes

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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© 2016 Mathematics Department | Imprint | Disclaimer | 17 May 2016