Introduction to Hodge theory
Author(s)
Bibliographic Information
Introduction to Hodge theory
（SMF/AMS texts and monographs, v. 8）（Panoramas et synthèses, no 3 (1996)）
American Mathematical Society, c2002
- : pbk
- Other Title
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Introduction à la théorie de Hodge
L2 Hodge theory and vanishing theorems
Available at / 36 libraries
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Science and Technology Library, Kyushu University
: pbk411.8/B 38031212010001181,
: pbk.023212002000544 -
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Note
"[2]" is superscript
"Société mathématique de France."
Includes bibliographical references (p. 229-232)
Contents of Works
- L[2] Hodge theory and vanishing theorems / Jean-Pierre Dmailly
- Frobenius and Hodge degeneration / Luc Illusie
- Variations of Hodge structure, Calabi-Yau manifolds and mirror symmetry / José Bertin, Chris Peters
Description and Table of Contents
Description
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: $L^2$ 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 natural starting points. Each of the three chapters is supplemented with a detailed introduction and numerous references. The reader will find precise statements of quite a number of open problems that have been the subject of active research in recent years. 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.
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.
by "Nielsen BookData"