Period mappings and period domains /
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 tha...
| Main Authors: | , , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
[2017]
Cambridge, United Kingdom : 2017 Cambridge, United Kingdom ; New York, NY : 2017 |
| Edition: | Second edition |
| Series: | Cambridge studies in advanced mathematics ;
168 Cambridge studies in advanced mathematics ; 168 |
| Subjects: |
| Summary: | 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{u2013}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{u2013}Tate groups and their associated domains, the Mumford{u2013}Tate varieties and generalizations of Shimura varieties.--Provided by publisher |
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| Item Description: | Previous edition: 2003 |
| Physical Description: | pages cm xiv, 562 pages : illustrations ; 23 cm xiv, 562 pages : illustrations ; 24 cm xiv, 562 pages ; 23 cm |
| Bibliography: | Includes bibliographical references (pages 540-555) and index Includes bibliographical references and index |
| ISBN: | 1107189861 (alk. paper) 1108422624 1316639568 9781107189867 (alk. paper) 9781108422628 9781316639566 |