Complex Manifolds (AMS Chelsea Publishing) by James Morrow and Kunihiko Kodaira (PDF)

Description

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.

User’s Reviews

Editorial Reviews: 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

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I would like to give this book a four-star rating but the number of errors/typos is truly astounding. There is an errata list at the back but, unfortunately, it is woefully inadequate. The book may lack exercises but that is no shortcoming for the diligent reader who will be sufficiently occupied with the task of correcting the text.Be aware that the book is not entirely self-contained. Some of the examples assume a knowledge of compact Riemann surfaces, reference is made to the explicit maps that define the Cech-de Rham isomorphisms and one should be familiar with quadric transformations and divisors, for instance.One further thing of note is that the authors take a classical “low brow” approach to the material: everything is developed in coordinates, rather than the modern coordinate-free language one would find in a book such as Wells’. This is not to disparage their work. A thorough understanding of the material, I believe, is only gained through a familiarity with both formalisms.Finally we mention that one of the authors – Kodaira – was a Field’s medalist and much of the latter part of the book deals with his original contributions to the subject.

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