This volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kähler manifolds called Hodge manifolds is algebraic. Included are the semicontinuity theorems and the local completeness theorem of Kuranishi. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds.

Table of Contents

Chapter 1. Definitions and Examples of Complex Manifolds

Chapter 2. Sheaves and Cohomology

Chapter 3. Geometry of Complex Maoifolds

Chapter 4. Applications of Elliptic Partial Differential Equations to Deformations

Review

"There is no question that this beautifully constructed book, full of elegant (and very economical) arguments underscores Abel's aforementioned dictum. Perhaps especially today, when so much is asked of the student of this material in the way of prerequisites, one can do no better than to turn to a master." ---- MAA Reviews

"There is no question that this beautifully constructed book, full of elegant (and very economical) arguments underscores Abel's aforementioned dictum." ---- MAA Reviews