Period mappings and period domains.

Carlson, James A. et al.

Cambridge U. Pr.

2003

430 pages

$90.00

Hardcover

Cambridge studies in advanced mathematics; 85

QA546

Carlson (U. of Utah) together with Stefan Muller-Stach (U. of Mainz, Germany), and Chris Peters (U. of Grenoble, France) have written a graduate textbook for students who have a knowledge of complex algebraic manifolds, algebraic topology, and differential geometry that offers a full discussion of the theory of period maps as this was developed by Phillip Griffiths (they include a lengthy bibliography). Each chapter includes an introductory outline, many examples and problems, and concluding remarks bringing the theory into a historical context. Basic theory is presented at length before turning to algebraic methods and finally to differential geometric methods. Appendices are included on projective varieties and complex manifolds, homology and cohomology, and vector bundles and Chern classes.

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