Synopses & Reviews
The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.
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
The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.
Table of Contents
Contents: Introduction; I. Local Theory of Complex Spaces by R.Remmert, II. Differential Calculus, Holomorphic Maps and Linear Structures on Complex Spaces by Th.Peternell and R.Remmert; III. Cohomology by Th.Peternell; IV. Seminormal Complex Spaces by G.Dethloff and H.Grauert; V. Pseudoconvexity, the Levi Problem and Vanishing Theorems by Th.Peternell; VI. Theory of q-Convesity and q-Concavity by H.Grauert; VII. Modifications by Th.Peternell; VIII. Cycle Spaces by F.Campana and Th.Peternell; IX. Extensions of Analytic Objects by H.Grauert and R.Remmert; Author Index, Subject Index