Complex Manifolds and Deformation of Complex Structures
Kodaira is a Fields Medal Prize Winner. (In the absence of a Nobel prize in mathematics, they are regarded as the highest professional honour a mathematician can attain.)\ Kodaira is an honorary member of the London Mathematical Society.\ Affordable softcover edition of 1986 classic
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From the reviews:"The author, [...], has written a book which will be of service to all who are interested in this by now vast subject. [...] This is a book of many virtues: mathematical, historical, and pedagogical. Parts of it could be used for a graduate complex manifolds course.J.A. Carlson in Mathematical Reviews, 1987"There are many mathematicians, or even physicists, who would find this book useful and accessible, but its distinctive attribute is the insight it gives into a brilliant mathematician's work. [...] It is intriguing to sense between the lines Spencer's optimism, Kodaira's scepticism or the shadow of Grauert with his very different methods, as it is to hear of the surprises and ironies which appeared on the way. Most of all it is a piece of work which shows mathematics as lying somewhere between discovery and invention, a fact which all mathematicians know, but most inexplicably conceal in their work."N.J. Hitchin in the Bulletin of the London Mathematical Society, 1987
Ch. 1Holomorphic functions1Ch. 2Complex manifolds28Ch. 3Differential forms, vector bundles, sheaves76Ch. 4Infinitesimal deformation182Ch. 5Theorem of existence209Ch. 6Theorem of completeness284Ch. 7Theorem of stability320AppElliptic partial differential operators on a manifold363
