A Guide To French Literature: Early Modern to Postmodern

Palgrave Macmillan, 15 août 1997 - 361 pages
The period matrix of a curve effectively describes how the complex structure varies; this is Torelli's theorem dating from the beginning of the previous century. In the 1950ies 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 1960ies and 1970ies 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 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. The basic theory of the period map as developed by Griffiths is developed in the first part of the book.

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