Grauert / Peternell / Remmert Several Complex Variables VII

Sheaf-Theoretical Methods in Complex Analysis
Erscheinungsjahr 2013
ISBN: 978-3-662-09873-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 74, 372 Seiten, eBook

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Grauert, H.

Peternell, Thomas

Remmert, R.

Weitere Mitwirkende

Campana, F.

Dethloff, G.

Grauert, H.

Peternell, Thomas

Remmert, R.

Inhaltsverzeichnis

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.