Hodge theory and period maps
This course introduces Hodge theory and period maps, which lie at the intersection of complex geometry, algebraic geometry, and arithmetic. Starting from the Hodge decomposition of the cohomology of smooth complex algebraic varieties, we develop variations of Hodge structure and their basic properties. We then study period domains and period maps, which encode how Hodge structures vary in families, and explore their geometric and arithmetic significance.
Lecturer
Date
10th March ~ 9th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 08:50 - 12:15 | A3-1a-205 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
Basic knowledge of complex manifolds.
Syllabus
(1) Hodge theory on complex manifolds
(2) Albanese and jacobian manifolds
(3) Sheaves and their cohomology
(4) De Rham complexes
(5) The Hodge structure on a hypersurface
(2) Albanese and jacobian manifolds
(3) Sheaves and their cohomology
(4) De Rham complexes
(5) The Hodge structure on a hypersurface
Reference
[1] E. Looijenga, Hodge theory and period maps, 2020, available at https://webspace.science.uu.nl/~looij101/CoursenotesHodge.pdf
[2] R.O. Wells, Jr: Differential Analysis on Complex Manifolds.
[3] Ph. Griffiths, J. Harris: Principles of Algebraic Geometry.
[4] Ph. Griffiths, On the periods of certain rational integrals I, II, Ann. of Math. 90 (1969), 460-495, 496-541.
[5] H. Clemens, Ph. Griffiths: The intermediate Jacobian of the cubic threefold. Ann. of Math. 95 (1972), 281–356.
[2] R.O. Wells, Jr: Differential Analysis on Complex Manifolds.
[3] Ph. Griffiths, J. Harris: Principles of Algebraic Geometry.
[4] Ph. Griffiths, On the periods of certain rational integrals I, II, Ann. of Math. 90 (1969), 460-495, 496-541.
[5] H. Clemens, Ph. Griffiths: The intermediate Jacobian of the cubic threefold. Ann. of Math. 95 (1972), 281–356.
Video Public
Yes
Notes Public
No
Language
English
Lecturer Intro
Dali Shen is an assistant professor at BIMSA currently. His research is focused on algebraic geometry and complex geometry. He obtained his PhD from Utrecht University. Before joining BIMSA, he held postdoc positions at IMPA and TIFR.