Period mappings and period domains /
The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby...
Main Author: | |
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Other Authors: | , , |
Format: | Book |
Language: | English |
Published: |
Cambridge ; New York :
Cambridge University Press,
2003
Cambridge, U.K. ; New York : 2003 Cambridge, U.K. ; New York : c2003 Cambridge, UK ; New York : 2003 Cambridge, UK ; New York : 2003 |
Series: | Cambridge studies in advanced mathematics ;
85 Cambridge studies in advanced mathematics Cambridge studies in advanced mathematics; 85 Cambridge studies in advanced mathematics ; 85 Cambridge studies in advanced mathematics 85 Cambridge studies in advanced mathematics |
Subjects: |
Table of Contents:
- Pt. I Basic Theory of the Period Map
- 1. Introductory Examples
- 2. Cohomology of Compact Kahler Manifolds
- 3. Holomorphic Invariants and Cohomology
- 4. Cohomology of Manifolds Varying in a Family
- 5. Period Maps Looked at Infinitesimally
- Pt. II. The Period Map: Algebraic Methods
- 6. Spectral Sequences
- 7. Koszul Complexes and Some Applications
- 8. Further Applications: Torelli Theorems for Hypersurfaces
- 9. Normal Functions and Their Applications
- 10. Applications to Algebraic Cycles: Nori's Theorem
- Pt. III. Differential Geometric Methods
- 11. Further Differential Geometric Tools
- 12. Structure of Period Domains
- 13. Curvature Estimates and Applications
- 14. Harmonic Maps and Hodge Theory
- App. A. Projective Varieties and Complex Manifolds
- App. B. Homology and Cohomology
- App. C. Vector Bundles and Chern Classes.
- Pt. I Basic Theory of the Period Map
- 1. Introductory Examples
- 2. Cohomology of Compact Kahler Manifolds
- 3. Holomorphic Invariants and Cohomology
- 4. Cohomology of Manifolds Varying in a Family
- 5. Period Maps Looked at Infinitesimally
- Pt. II. The Period Map: Algebraic Methods
- 6. Spectral Sequences
- 7. Koszul Complexes and Some Applications
- 8. Further Applications: Torelli Theorems for Hypersurfaces
- 9. Normal Functions and Their Applications
- 10. Applications to Algebraic Cycles: Nori's Theorem
- Pt. III. Differential Geometric Methods
- 11. Further Differential Geometric Tools
- 12. Structure of Period Domains
- 13. Curvature Estimates and Applications.
- pt. I Basic Theory of the Period Map
- 1. Introductory Examples
- 2. Cohomology of Compact Kahler Manifolds
- 3. Holomorphic Invariants and Cohomology
- 4. Cohomology of Manifolds Varying in a Family
- 5. Period Maps Looked at Infinitesimally
- pt. II. The Period Map: Algebraic Methods
- 6. Spectral Sequences
- 7. Koszul Complexes and Some Applications
- 8. Further Applications: Torelli Theorems for Hypersurfaces
- 9. Normal Functions and Their Applications
- 10. Applications to Algebraic Cycles: Nori's Theorem
- pt. III. Differential Geometric Methods
- 11. Further Differential Geometric Tools
- 12. Structure of Period Domains
- 13. Curvature Estimates and Applications.