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...

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Bibliographic Details
Main Author:	Carlson, James A., 1946-
Other Authors:	Müller-Stach, Stefan, 1962-, Müller-Stach, Stefan, 1962-, Peters, C (Chris)
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:	Geometry, Algebraic Hodge theory Torelli theorem

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.

Period mappings and period domains /

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