Transcendental Methods in the Study of Algebraic Cycles

Abstract

In these lectures, in contrast with the orientation of M. Green’s lectures, we put the accent on the global arguments used when working with families of algebraic varieties (monodromy arguments), and also on the relations between non representability of Chow groups and the “transeendental part of Hodge structures”, which explains the title, excepted for the fact that there are very few things that cannot be done within algebraic geometry.

Each lecture is introduced, and they are independent, excepted for lecture 5 - lecture 6, and lecture 7 - lecture 8. The lectures should be read in parallel with those of M. Green and J.P. Murre which they are supposed to complete. They are organized as follows:

• 1. Divisors

• 2. Topology and Hodge theory

• 3. Noether-Lefschetz locus

• 4. Monodromy

• 5. 0-cycles I

• 6. 0-cycles II

• 7. Griffiths groups

• 8. Application of the Noether-Lefschetz locus to threefolds.