Introduction to Hodge Theory

By: Jose Bertin, Jean-Pierre Demailly, Luc Illusie, Chris Peters

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Paperback | 1 April 2002

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Hodge 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 incharacteristicp$, 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.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Topology Algebraic Topology Algebra Geometry Algebraic Geometry Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory

Applied Mathematics Mathematical Foundation Set Theory

$L^2$ Hodge theory and vanishing theorems
Frobenius and Hodge degeneration
Variations of Hodge structure, Calabi-Yau manifolds and mirror symmetry
Table of Contents provided by Publisher. All Rights Reserved.

Introduction to Hodge Theory

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