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OverviewHodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry. This book consists of expositions of various aspects of modern Hodge theory. Its purpose is to provide the nonexpert reader with a precise idea of the current status of the subject. The three chapters develop distinct but closely related subjects: $L2$ Hodge theory and vanishing theorems; Frobenius and Hodge degeneration; variations of Hodge structures and mirror symmetry. The techniques employed cover a wide range of methods borrowed from the heart of mathematics: elliptic PDE theory, complex differential geometry, algebraic geometry in characteristic $p$, cohomological and sheaf-theoretic methods, deformation theory of complex varieties, Calabi-Yau manifolds, singularity theory, etc. A special effort has been made to approach the various themes from their most na The reader should have some familiarity with differential and algebraic geometry, with other prerequisites varying by chapter. The book is suitable as an accompaniment to a second course in algebraic geometry. Full Product DetailsAuthor: Jose Bertin , Jean-Pierre Demailly , Luc Illusie , Chris PetersPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 8 Dimensions: Width: 17.50cm , Height: 1.50cm , Length: 18.00cm Weight: 0.460kg ISBN: 9780821820407ISBN 10: 0821820400 Pages: 232 Publication Date: 30 April 2002 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents$L^2$ Hodge theory and vanishing theorems by J.-P. Demailly Frobenius and Hodge degeneration by L. Illusie Variations of Hodge structure, Calabi-Yau manifolds and mirror symmetry by J. Bertin and C. Peters.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |