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Several Complex Variables VII

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  • 372 Seiten
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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... Weiterlesen
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Beschreibung

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.

This volume of the Encyclopaedia offers a systematic introduction and a comprehensive survey of the theory of complex spaces. This is an important subject in the theory of several complex variables. Two of the authors, Grauert and Remmert, are internationally known outstanding experts who have developed substantial parts of the field. The authors have written for graduate students and researchers in complex analysis, algebraic geometry and differential geometry. The book will also be a valuable source of information for mathematical physicists.

Autorentext
Hans Grauert studierte in Münster und Zürich, wo er 1958 promovierte. Seit dem 1. Oktober 1959 war er bis zu seiner Emeritierung ordentlicher Professor in Göttingen. Er hatte Gastprofessuren u.a. in Princeton und Paris. Er gilt als einer der bedeutendsten deutschen Mathematiker der Nachkriegszeit. Sein Spezialgebiet ist die Funktionentheorie mehrerer 'Veränderlicher'.

Inhalt
I. Local Theory of Complex Spaces.- II. Differential Calculus, Holomorphic Maps and Linear Structures on Complex Spaces.- III. Cohomology.- IV. Seminormal Complex Spaces.- V. Pseudoconvexity, the Levi Problem and Vanishing Theorems.- VI. Theory of q-Convexity and q-Concavity.- VII. Modifications.- VIII. Cycle Spaces.- IX. Extension of Analytic Objects.- Author Index.

Produktinformationen

Titel: Several Complex Variables VII
Untertitel: Sheaf-Theoretical Methods in Complex Analysis
Editor:
Schöpfer:
EAN: 9783540562597
ISBN: 978-3-540-56259-7
Format: Fester Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 372
Gewicht: 680g
Größe: H27mm x B242mm x T163mm
Jahr: 1994
Auflage: 1994. 1994

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