Several Complex Variables VII

Sheaf-Theoretical Methods in Complex Analysis

H. Grauert, Thomas Peternell, R. Remmert (Herausgeber)

Buch | Softcover

VIII, 372 Seiten

2010
Springer Berlin (Verlag)
978-3-642-08150-7 (ISBN)

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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 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.

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.

Erscheint lt. Verlag	19.10.2010
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Co-Autor	F. Campana, G. Dethloff, H. Grauert, Thomas Peternell, R. Remmert
Zusatzinfo	VIII, 372 p.
Verlagsort	Berlin
Sprache	englisch
Maße	152 x 229 mm
Gewicht	571 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Analysis • Calculus • coherent sheaves • cohomology • Complex Analysis • Complex spaces • convexity and concavity • Kohärente Garben • Kohomologie • komplexe Räume • Konvexität und Konkavität • modifications • Modifikation • Pseudoconvexity
ISBN-10	3-642-08150-9 / 3642081509
ISBN-13	978-3-642-08150-7 / 9783642081507
Zustand	Neuware