Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis (Encyclopaedia of Mathematical Sciences) (v. 7)

ISBN 10: 3540562591 / ISBN 13: 9783540562597

Published by Springer, 1994

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Bibliographic Details

• Title: Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis (Encyclopaedia of Mathematical Sciences) (v. 7)
• Publisher: Springer
• Publication Date: 1994
• Language: English
• ISBN 10: 3540562591
• ISBN 13: 9783540562597
• Binding: Hardcover
• Condition: Like New
• Book Type: book

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Synopsis

Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g­ dimensional complex torus to X. If 9 ~ 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, ... , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.

Synopsis

This volume of the Encyclopaedia offers a systematic introduction and a comprehensive survey of the theory of complex spaces. It covers topics like semi-normal complex spaces, cohomology, the Levi problem, q-convexity and q-concavity. It is the first survey of this kind. The authors are internationally known outstanding experts who developed substantial parts of the field. The book contains seven chapters and an introduction written by Remmert, describing the history of the subject. The book will be very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry. Another group of readers will consist of mathematical physicists who apply results from these fields.