nLab Hodge theory and Complex algebraic geometry


This page collects material related to the textbook

on Hodge theory and GAGA.


Volume 1

I Preliminaries

1 Holomorphic functions of many variables

2. Complex manifold

3. Kähler metric

4. Sheaves and cohomology

II The Hodge decomposition

5. Harmonic forms and cohomology

6. The case of Kähler manifolds

7. Hodge structures and polarization

8. Holomorphic de Rham complexes and spectral sequences

III Variations of Hodge structures

9. Families and deformations

10. Variations of Hodge structure

IV. Cycles and cycle classes

11. Hodge classes

12. Deligne-Beilinson cohomology and the Abel-Jacobi map

Volume 2


category: reference

Last revised on July 25, 2021 at 12:39:38. See the history of this page for a list of all contributions to it.