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.
讲师
日期
2026年03月10日 至 06月09日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 08:50 - 12:15 | A3-1a-205 | ZOOM 05 | 293 812 9202 | BIMSA |
修课要求
Basic knowledge of complex manifolds.
课程大纲
(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
参考资料
[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.
视频公开
公开
笔记公开
不公开
语言
英文
讲师介绍
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.