10% off all books and free delivery over £40
Buy from our bookstore and 25% of the cover price will be given to a school of your choice to buy more books. *15% of eBooks.

Period Mappings and Period Domains

View All Editions

The selected edition of this book is not available to buy right now.
Add To Wishlist
Write A Review

About

Period Mappings and Period Domains Synopsis

This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether–Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford–Tate groups and their associated domains, the Mumford–Tate varieties and generalizations of Shimura varieties.

About This Edition

ISBN: 9781316639566
Publication date: 11th August 2017
Author: James (University of Utah) Carlson, Stefan (Johannes Gutenberg Universität Mainz, Germany) Müller-Stach, Chris Peters
Publisher: Cambridge University Press
Format: Paperback
Pagination: 576 pages
Series: Cambridge Studies in Advanced Mathematics
Genres: Geometry