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401-8146-DRL 3 Credits DR D-MATH

Hodge Theory and Algebraic Cycles, part 2 (University of Zurich)

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Last Updated: 2026-02-05 16:37:27

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
DR

Examination

Type
ungraded semester performance
Registration modalities, date and venue of this performance assessment are specified solely by the UZH.

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