Analytic Function Theory of Several Variables

Elements of Oka’s Coherence

Junjiro Noguchi (Autor)

Buch | Hardcover

397 Seiten

2016 | 1st ed. 2016
Springer Verlag, Singapore
978-981-10-0289-2 (ISBN)

Artikel merken

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps).The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later.The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka–Cartan's Fundamental Theorem (Chap. 4); Coherence of ideal sheaves of complex analytic subsets (Chap. 6); Coherence of the normalization sheaves of complex spaces (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domains (Chap. 8). The theories of sheaf cohomology and domains of holomorphy are also presented (Chaps. 3, 5). Chapter 6 deals with the theory of complex analytic subsets. Chapter 8 is devoted to the applications of formerly obtained results, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. 9, we discuss the historical development of "Coherence".It is difficult to find a book at this level that treats all of the above subjects in a completely self-contained manner. In the present volume, a number of classical proofs are improved and simplified, so that the contents are easily accessible for beginning graduate students.

Holomorphic Functions.- Oka's First Coherence Theorem.- Sheaf Cohomology.- Holomorphically Convex Domains and Oka--Cartan's Fundamental Theorem.- Domains of Holomorphy.- Analytic Sets and Complex Spaces.- Pseudoconvex Domains and Oka's Theorem.- Cohomology of Coherent Sheaves and Kodaira's Embedding Theorem.- On Coherence.- Appendix.- References.- Index.- Symbols.

Erscheinungsdatum	01.03.2016
Zusatzinfo	116 Illustrations, black and white; XVI, 397 p. 116 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Holomorphic Functions • Oka--Cartan’s fundamental theorem • Oka’s first coherence theorem • Oka’s theorem • pseudoconvex domains
ISBN-10	981-10-0289-4 / 9811002894
ISBN-13	978-981-10-0289-2 / 9789811002892
Zustand	Neuware