Lectures on Complex Analytic Varieties: Finite Analytic Mappings. (MN-14)

Lectures on Complex Analytic Varieties: Finite Analytic Mappings. (MN-14)

ROBERT C. GUNNING
Copyright Date: 1974
Pages: 165
https://www.jstor.org/stable/j.ctt130hk90
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  • Book Info
    Lectures on Complex Analytic Varieties: Finite Analytic Mappings. (MN-14)
    Book Description:

    This book is a sequel toLectures on Complex Analytic Varieties: The Local Paranwtrization Theorem(Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappings in one complex dimension. The purpose of this volume is rather to clarify some algebraic aspects of the local study of complex analytic varieties than merely to examine finite analytic mappings for their own sake.

    Originally published in 1974.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6929-9
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. None)
  2. PREFACE
    (pp. i-i)
    R. C. Gunning
  3. Table of Contents
    (pp. ii-ii)
  4. §1. Finite analytic mappings
    (pp. 1-37)

    (a) These notes are intended as a sequel to the lecture notes [symbol], so it will be assumed from the outset that the reader is somewhat familiar with the contents of the earlier notes and the notation and terminology introduced in those notes will generally be used here without further reference. It will also be assumed that the reader has some background knowledge of the theory of functions of several complex variables and of the theory of sheaves, at least to the extent outlined at the beginning of the earlier notes. For clarity and emphasis however a brief introductory review...

  5. §2. Finite analytic mappings with given domain
    (pp. 38-85)

    (a) Consider the problem of describing all finite analytic mappings from a given germ V of a complex analytic variety into another germ of complex analytic variety. The image of any such mapping is itself a germ of a complex analytic variety as a consequence of Theorem 2, so the mapping can be viewed as the composition of a surjective finite analytic mapping and an inclusion mapping; and the present interest centers on describing only the first of these two factors. If φ: V → W is a surjective finite analytic mapping then the induced homomorphism φ*:Wθ →Vθ...

  6. §3. Finite analytic mappings with given range.
    (pp. 86-143)

    (a) Consider next the problem of describing all finite analytic mappings from germs of complex analytic varieties to a given germ V of a complex analytic variety. If φ: W → V is a finite analytic mapping the induced homomorphism φ*:Vθ →Wθ can be viewed as exhibitingWθ as a finitely generatedVθ-module; conversely ifWθ has the structure of a finitely generatedVθ-module then the mapping φ*:Vθ →Wθ defined by φ*(f) = f·1 ∈Wθ is clearly a finite homomorphism of complex algebras preserving the identities, and by Theorem 3(b) this is the homomorphism induced...

  7. Appendix. Local cohomology groups of complements of complex analytic subvarieties.
    (pp. 144-159)
  8. INDEX OF SYMBOLS
    (pp. 160-160)
  9. INDEX
    (pp. 161-163)
  10. Back Matter
    (pp. 164-164)