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"During 1981-1982 the Institute for Advanced Study held a special year on algebraic geometry. Naturally there were a number of seminars, and this volume is essentially the proceedings of one of these. The motif of the seminar was to explore the ways in which the recent developme…
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-t…
This monograph gives an exposition of Hodge theory, leading to three new proofs of a local Torelli theorem for curves and a proof for a smooth family of surfaces, threefolds, or fourfolds, whose cotangent map is a birational morphism.