عنوان

Period mappings and period domains /

شابک

0521814669

شابک

9780521814669

شماره

dltt

عنوان اصلي

Period mappings and period domains /

نام عام مواد

[Book]

نام نخستين پديدآور

James Carlson, Stefan Müller-Stach, Chris Peters

نام خاص و کميت اثر

xvi, 430 pages :

ساير جزييات

illustrations ;

ابعاد

24 cm

عنوان فروست

Cambridge studies in advanced mathematics ;

مشخصه جلد

85

متن يادداشت

Includes bibliographical references (pages 415-425) and index

متن يادداشت

The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelov-type theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold

موضوع مستند نشده

Geometry, Algebraic

موضوع مستند نشده

Hodge theory

موضوع مستند نشده

Torelli theorem

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Carlson, James A.,1946-

مستند نام اشخاص تاييد نشده

Müller-Stach, Stefan,1962-

مستند نام اشخاص تاييد نشده

Peters, C., (Chris)

تاريخ عمليات

20160712072225.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y