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Inhaltsangabe: Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string models and are thus being studied vigorously in the recent physics literature. In the main part of the Book, collected and reviewed are relevant results on (1) several major techniques of constructing such spaces and (2) computation of physically relevant quantities such as massless field spectra and their Yukawa interactions. Issues of (3) stringy corrections and (4) moduli space and its geometry are still in the stage of rapid and continuing development, whence there is more emphasis on open problems here. Also is included a preliminary discussion of the conjectured universal moduli space and related open problems. Finally, several detailed models and sample computations are included throughout the Book to exemplify the techniques and the general discussion.The Book also contains a Lexicon (28 pages) of 150 assorted terms, key-words and main results and theorems, well suited for a handy reference. Although cross-referenced with the main part of the Book, the Lexicon can also be used independently.The level of mathematics is guided and developed between that of the popular Physics Reports of Eguchi, Gilkey and Hanson and the book Superstrings (Vol. 2) by Green, Schwarz and Witten on one end and Principles of Algebraic Geometry of Griffiths and Harris on the other.This is the first systematic exposition in book form of the material on Calabi-Yau spaces, related mathematics and the physics application, otherwise scattered through research articles in journals and conference proceedings.
Review: "Hubsch has patiently collected and described a sometimes bewilderingly large number of relevant techniques from differential geometry and he thoroughly works out some quite illuminating examples, including many of physical interest ... His explanations are generally thorough and clear ... Hubsch's exposition is engaging and entertaining ... In the final section, Hubsch offers a tantalizing introduction to the many remarkable quantum properties of Calabi-Yau sigma models discovered in the last few years." Edward Witten Physics Today, 1993 "The book by Hubsch is the first and only available monography, bringing together the mathematical results and presenting them in a form useful for the physicists. It is written in a light vein and often manages to simplify the mathematics, making them more palatable to physics users. An essential tool for workers on strings, supergravity and related topics." Yuval Ne'eman Tel Aviv Univ., 1992 "This book is full of interesting and illustrative examples. Here one can see the techniques and theorems of algebraic geometry in action. It is also written with a great deal of style. Though apparently for physicists, I would highly recommend it for mathematicians and especially for students of algebraic geometry. It is not easy to write for both mathematicians and physicists -- I would say that this is an admirable example of such writing. Reading it, you will find that these manifolds are truly exciting creatures." Michael Eastwood University of Adelaide, 1992
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