Period Mappings and Period Domains

Part I. Basic Theory:
1. Introductory examples
2. Cohomology of compact Kähler manifolds
3. Holomorphic invariants and cohomology
4. Cohomology of manifolds varying in a family
5. Period maps looked at infinitesimally
Part II. Algebraic Methods:
6. Spectral sequences
7. Koszul complexes and some applications
8. Torelli theorems
9. Normal functions and their applications
10. Applications to algebraic cycles: Nori's theorem
Part III. Differential Geometric Aspects:
11. Further differential geometric tools
12. Structure of period domains
13. Curvature estimates and applications
14. Harmonic maps and Hodge theory
Part IV. Additional Topics:
15. Hodge structures and algebraic groups
16. Mumford–Tate domains
17. Hodge loci and special subvarieties
Appendix A. Projective varieties and complex manifolds
Appendix B. Homology and cohomology
Appendix C. Vector bundles and Chern classes
Appendix D. Lie groups and algebraic groups
References
Index.