Period Mappings and Period Domains

Name: Period Mappings and Period Domains
Brand: Cambridge University Press
SKU: 9781316639566
Price: 61.74 EUR
Availability: InStock

★★★★★

English

By (author): Chris Peters James Carlson Stefan Muller-Stach

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 NoetherLefschetz 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 MumfordTate groups and their associated domains, the MumfordTate varieties and generalizations of Shimura varieties. See more

€61.74

€64.99

Save 5%

Quantity

A01=Chris PetersA01=James CarlsonA01=Stefan Muller-StachAge Group_UncategorizedAuthor_Chris PetersAuthor_James CarlsonAuthor_Stefan Muller-Stachautomatic-updateCategory1=Non-FictionCategory=PBKBCategory=PBKDCategory=PBMWCOP=United KingdomDelivery_Delivery within 10-20 working daysLanguage_EnglishPA=In stockPrice_€50 to €100PS=Activesoftlaunch

Delivery/Collection within 10-20 working days

Product Details

Weight: 820g
Dimensions: 153 x 227mm
Publication Date: 11 Aug 2017
Publisher: Cambridge University Press
Publication City/Country: United Kingdom
Language: English
ISBN13: 9781316639566

About Chris PetersJames CarlsonStefan Muller-Stach

James Carlson is Professor Emeritus at the University of Utah. From 2003 to 2012 he was president of the Clay Mathematics Institute New Hampshire. Most of Carlson's research is in the area of Hodge theory. Stefan Müller-Stach is Professor of number theory at Johannes Gutenberg Universität Mainz Germany. He works in arithmetic and algebraic geometry focussing on algebraic cycles and Hodge theory and his recent research interests include period integrals and the history and foundations of mathematics. Recently he has published monographs on number theory (with J. Piontkowski) and period numbers (with A. Huber) as well as an edition of some works of Richard Dedekind. Chris Peters is a retired professor from the Université Grenoble Alpes France and has a research position at the Eindhoven University of Technology The Netherlands. He is widely known for the monographs Compact Complex Surfaces (with W. Barth K. Hulek and A. van de Ven 1984) as well as Mixed Hodge Structures (with J. Steenbrink 2008). He has also written shorter treatises on the motivic aspects of Hodge theory on motives (with J. P. Murre and J. Nagel) and on applications of Hodge theory in mirror symmetry (with Bertin).