Hodge Theory and Complex Algebraic Geometry I, Volume 1by Claire Voisin, C. Voisin
Pub. Date: 08/28/2007
Publisher: Cambridge University Press
The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students. See more details below
The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.
Table of Contents
Introduction; Part I. Preliminaries: 1. Holomorphic functions of many variables; 2. Complex manifolds; 3. Kähler metrics; 4. Sheaves and cohomology; Part II. The Hodge Decomposition: 5. Harmonic forms and cohomology; 6. The case of Kähler manifolds; 7. Hodge structures and polarisations; 8. Holomorphic de Rham complexes and spectral sequences; Part III. Variations of Hodge Structure: 9. Families and deformations; 10. Variations of Hodge structure; Part IV. Cycles and Cycle Classes: 11. Hodge classes; 12. Deligne-Beilinson cohomology and the Abel-Jacobi map; Bibliography; Index.
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