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Period mappings and period domains

Carlson, James A., (1946-)

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Period mappings and period domains

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Period mappings and period domains/ James Carlson, Stefan Muller-Stach, Chris Peters.
作者:	Carlson, James A.,
其他作者:	Muller-Stach, Stefan,
出版者:	Cambridge :Cambridge University Press, : 2017.,
面頁冊數:	xiv, 562 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 30 Aug 2017).
標題:	Geometry, Algebraic. -
電子資源:	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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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.
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