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Period mappings and period domains

Carlson, James A., (1946-)

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Period mappings and period domains

Record Type:	Electronic resources : Monograph/item
Title/Author:	Period mappings and period domains/ James Carlson, Stefan Muller-Stach, Chris Peters.
Author:	Carlson, James A.,
other author:	Muller-Stach, Stefan,
Published:	Cambridge :Cambridge University Press, : 2017.,
Description:	xiv, 562 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 30 Aug 2017).
Subject:	Geometry, Algebraic. -
Online resource:	https://doi.org/10.1017/9781316995846
ISBN:	9781316995846

Period mappings and period domains
Carlson, James A.,1946-

Period mappings and period domains[electronic resource] /James Carlson, Stefan Muller-Stach, Chris Peters. - Second edition. - Cambridge :Cambridge University Press,2017. - xiv, 562 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;168. - Cambridge studies in advanced mathematics ;168..

Title from publisher's bibliographic system (viewed on 30 Aug 2017).

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.

ISBN: 9781316995846Subjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564 / .C28 2017

Dewey Class. No.: 516.35

Period mappings and period domains
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020 $a 9781108422628 $q (hardback)
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100 1 $a Carlson, James A., $d 1946- $3 534345
245 1 0 $a Period mappings and period domains $h [electronic resource] / $c James Carlson, Stefan Muller-Stach, Chris Peters.
250 $a Second edition.
260 $a Cambridge : $b Cambridge University Press, $c 2017.
300 $a xiv, 562 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 168
500 $a Title from publisher's bibliographic system (viewed on 30 Aug 2017).
520 $a 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.
650 0 $a Geometry, Algebraic. $3 532048
650 0 $a Hodge theory. $3 701563
650 0 $a Torelli theorem. $3 701564
700 1 $a Muller-Stach, Stefan, $d 1962- $3 3470466
700 1 $a Peters, Chris. $3 3470467
830 0 $a Cambridge studies in advanced mathematics ; $v 168. $3 3470468
856 4 0 $u https://doi.org/10.1017/9781316995846