rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Analytic Function Theory of Several Variables
    sub title: Elements of Oka’s Coherence
  name:
    name part: Noguchi, Junjiro.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: si
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 397 p. 28 illus., 27 illus. in color. online resource.
  abstract: 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 a…
  table of contents: 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.
  note: by Junjiro Noguchi.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Category theory (Mathematics)
  subject:
    topic: Homological algebra
  subject:
    topic: Functions of complex variables
  subject:
    topic: Mathematics
  subject:
    topic: Several Complex Variables and Analytic Spaces
  subject:
    topic: Category Theory, Homological Algebra
  subject:
    topic: Algebraic Geometry
  classification: QA331.7
  classification: 515.94
  related item:
    title info:
      title: Springer eBooks
  identifier: 9789811002915
  identifier: http://dx.doi.org/10.1007/978-981-10-0291-5
  record info:
    record creation date: 160816
    record change date: 20161001141358.0
    record identifier: 978-981-10-0291-5