Misprints, additions

A review by W. Kleinert and by Gregory J. Pearlstein

CONTENTS

Part I Basic Theory of the Period Map

Chap. 1 Introductory Examples

Chap. 2 Cohomology of compact Kähler manifolds

Chap. 3 Holomorphic invariants and cohomology

Chap. 4 Cohomology of manifolds varying in a family

Chap.5 Period maps looked at infinitesimally

Part II: Algebraic Methods in the Study of the Period Map

Chap. 6 Spectral sequences

Chap. 7 Koszul complexes and some applications

Chap. 8 Further applications: Torelli theorems for hypersurfaces

Chap. 9 Normal functions and its applications

Chap. 10 Applications to algebraic cycles: Nori's theorem

Part III: Differential Geometric Methods

Chapt. 11 Further differential geometric tools

Chap. 12 Structure of Period Domains

Chap. 13 Curvature estimates and applications

Chap. 14 Harmonic Maps and Hodge Theory

Appendices

Projective varieties and complex manifolds

Homology and cohomology

Vector bundles and Chern classes