Introduction to Hodge Theory (SMF/AMS Texts and Monographs) - Image 1

£61.86

Brand: Amer Mathematical Society Introduction to Hodge Theory (SMF/AMS Texts and Monographs)

Name: Introduction to Hodge Theory (SMF/AMS Texts and Monographs)
Brand: Brand: Amer Mathematical Society
Price: 64.12 GBP
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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.

Product Specifications

Brand: Brand: Amer Mathematical Society
Format: Paperback
ASIN: 0821820400
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 20 June 2002
Listed Since: 10 December 2006

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Brand: Amer Mathematical Society Introduction to Hodge Theory (SMF/AMS Texts and Monographs)

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