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Catalogue Information
Field name	Details
Dewey Class	515.9
Title	Several Complex Variables VII ([EBook] :) : Sheaf-Theoretical Methods in Complex Analysis / / edited by H. Grauert, Th. Peternell, R. Remmert.
Added Personal Name	Grauert, H. editor.
	Peternell, Th editor.
	Remmert, R. editor.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1994.
Physical Details	VIII, 372 p. : online resource.
Series	Encyclopaedia of mathematical sciences 0938-0396 ; ; 74
ISBN	9783662098738
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-09873-8
Links to Related Works	Subject References: Algebraic Geometry . Analysis . Analysis (Mathematics) . Differential Geometry . Functions of a Complex Variable . Functions of complex variables . Mathematical analysis . Mathematics . Physics . Theoretical, Mathematical and Computational Physics . Authors: Grauert, H. . Peternell, Th . Remmert, R. . Corporate Authors: SpringerLink (Online service) . Series: Encyclopaedia of mathematical sciences . Classification: 515.9 .

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Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis /

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