Claire Voisin (Paris Centre de Mathematiques de Jussieu)

Hodge Theory and Complex Algebraic Geometry I

• Broschiertes Buch

Produktbeschreibung

This is a completely self-contained modern introduction to Kaehlerian geometry and Hodge structure. The author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. Aimed at students, the text is complemented by exercises which provide useful results in complex algebraic geometry.

Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• Seitenzahl: 334
• Erscheinungstermin: 12. Januar 2011
• Englisch
• Abmessung: 229mm x 152mm x 20mm
• Gewicht: 506g
• ISBN-13: 9780521718011
• ISBN-10: 0521718015
• Artikelnr.: 23498045

Autorenporträt

Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France

Inhaltsangabe

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.