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Period Mappings and Period Domains - Cambridge Studies in Advanced Mathematics 85 (Paperback)
  • Period Mappings and Period Domains - Cambridge Studies in Advanced Mathematics 85 (Paperback)

Period Mappings and Period Domains - Cambridge Studies in Advanced Mathematics 85 (Paperback)

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Paperback 446 Pages / Published: 17/01/2013
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The period matrix of a curve effectively describes how the complex structure varies; this is Torelli's theorem dating from the beginning of the nineteenth century. In the 1950s during the first revolution of algebraic geometry, attention shifted to higher dimensions and one of the guiding conjectures, the Hodge conjecture, got formulated. In the late 1960s and 1970s Griffiths, in an attempt to solve this conjecture, generalized the classical period matrices introducing period domains and period maps for higher-dimensional manifolds. He then found some unexpected new phenomena for cycles on higher-dimensional algebraic varieties, which were later made much more precise by Clemens, Voisin, Green and others. This 2003 book presents this development starting at the beginning: the elliptic curve. This and subsequent examples (curves of higher genus, double planes) are used to motivate the concepts that play a role in the rest of the book.

Publisher: Cambridge University Press
ISBN: 9781107412774
Number of pages: 446
Dimensions: 229 x 152 mm

'The presentation of the vast material is very lucid and inspiring, methodologically well-planned and utmost user-friendly considering such sophisticated a complex of topics.' Zentralblatt fur Mathematik
'This book, dedicated to Philip Griffiths, provides an excellent introduction to the study of periods of algebraic integrals and their applications to complex algebraic geometry. In addition to the clarity of the presentation and the wealth of information, this book also contains numerous problems which render it ideal for use in a graduate course in Hodge theory.' Mathematical Reviews
'... generally more informal and differential-geometric in its approach, which will appeal to many readers. ... the book is a useful introduction to Carlos Simpson's deep analysis of the fundamental groups of compact Kahler manifolds using harmonic maps and Higgs bundles.' Burt Totaro, University of Cambridge

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