Period Mappings and Period Domains (Hardcover, 2nd Revised edition)

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 Kahler. 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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Cambridge Studies in Advanced Mathematics
Release date:	August 2017
Authors:	James Carlson • Stefan Muller-Stach • Chris Peters
Dimensions:	238 x 160 x 42mm (L x W x T)
Format:	Hardcover
Edition:	2nd Revised edition
ISBN-13:	978-1-108-42262-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	1-108-42262-4
Barcode:	9781108422628

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