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Abstract
Hodge theory is a powerful tool to study the cohomology of algebraic varieties. In this course, we will review the existence of the Hodge decomposition on the cohomology of smooth projective varieties.Following Deligne, we will explain how to generalise this to arbitrary varieties, using the notion of mixed Hodge structures. We then give several applications to the study of algebraic cycles.
Content
Hodge theory is a powerful tool to study the cohomology of algebraic varieties. In this course, we will review the existence of the Hodge decomposition on the cohomology of smooth projective varieties. Following Deligne, we will explain how to generalise this to arbitrary varieties, using the notion of mixed Hodge structures. We then give several applications to the study of algebraic cycles. In particular, we explain Griffiths’ construction of cycles which are homologically trivial but not algebraically trivial. We will also prove Nori’s connectivity theorem and give some of its applications.
Resources
Literature
Hodge Theory and Complex Algebraic Geometry, I & II, by Claire Voisin
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Hodge Theory and Algebraic Cycles, part 2 (University of Zurich) | No time listed | 4 h weekly |
| exercise | Hodge Theory and Algebraic Cycles, part 2 (University of Zurich) | No time listed | 2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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