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Complex manifolds and deformation of complex structures. Transl. from the Japanese by Kazuo Akao. (English) Zbl 0581.32012
Grundlehren der Mathematischen Wissenschaften, 283. New York etc.: Springer-Verlag. X, 465 p. DM 174.00 (1986).
This is a beautiful graduate textbook to study the theory of deformations of complex manifolds. It is basically self-contained. Three chapters are devoted to explain standard materials as holomorphic function, complex manifold, vector bundle, sheaf cohomology etc. The author also explains how he and D. Spencer reached the notion of deformations and gives enough examples. Further developments are also included. In the appendix, there is an introductory short course for the elliptic partial differential operators on manifolds by Daisuke Fujiwara.
Reviewer: M.Oka

MSC:
32Q99 Complex manifolds
32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
32-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces
32G10 Deformations of submanifolds and subspaces
32G05 Deformations of complex structures
58J10 Differential complexes