This book, a revision and organization of
lectures given by Kodaira at Stanford University in 1965–66, is an
excellent, well-written introduction to the study of abstract complex
(analytic) manifolds—a subject that began in the late 1940's and
early 1950's. It is largely self-contained, except for some standard
results about elliptic partial differential equations, for which
complete references are given.
—D. C. Spencer, MathSciNet
The book under review is the faithful reprint
of the original edition of one of the most influential textbooks in
modern complex analysis and geometry. The classic “Complex
Manifolds” by J. Morrow and K. Kodaira was first published in
1971 …, essentially as a revised and elaborated version of a set of
notes taken from lectures of Fields medallist Kunihiko Kodaira at
Stanford University in 1965–1966, and has maintained its role as
a standard introduction to the geometry of complex manifolds and their
deformations ever since.
—Werner Kleinert, Zentralblatt MATH
Of course everyone knows Abel's exhortation
that we should seek out “the masters, not their pupils,”
if we are to learn mathematics well and effectively. … 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
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.
Readership
Graduate students and research mathematicians
interested in abstract complex manifolds.
Download chapters as PDF