Complex Manifolds

The main purpose of this book is to give an introduction to the Kodaira-Spencer theory of deformations of complex structures. The original proof of the Kodaira embedding theorem is given 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. The book is based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966. Complete references are given for the results that are used from elliptic partial differential equations.

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 Kahler 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.