Introduction to Hodge Theory (SMF/AMS Texts & Monographs No. 8)

Introduction to Hodge Theory (SMF/AMS Texts & Monographs No. 8)

By: Jose Bertin (author), Jean-Pierre Demailly (author), Chris Peters (author), Luc Illusie (author)Paperback

1 - 2 weeks availability

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.

Create a review

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.

Product Details

  • publication date: 15/04/2002
  • ISBN13: 9780821820407
  • Format: Paperback
  • Number Of Pages: 232
  • ID: 9780821820407
  • weight: 430
  • ISBN10: 0821820400

Delivery Information

  • Saver Delivery: Yes
  • 1st Class Delivery: Yes
  • Courier Delivery: Yes
  • Store Delivery: Yes

Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly

Close