Skip to main content
SpringerLink
Log in

Relative komplexe quotienten

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Let π∶X→S be a holomorphic map, and let R⊂X×SX be an equivalence relation. The restriction of R to the fibre π−1(S) is denoted by Rs. The quotient X/R is called a relative complex quotient, if the quotient map X→X/R is holomorphic over S. Two cases are studied: (C) All fibres of π are locally Rs-separable (relative Cartan quotient); (R) All fibres of π are holomorphically convex, and Rs is given by tke holomorphic functions on π−1 (s) (relative Remmert quotient).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literatur

  1. Cartan, H., Quotients of Complex Analytic Spaces, in: Contributions to Function Theory. Tata Inst. of Fund. Research, Bombay, 1–15 (1960)

    Google Scholar 

  2. Fischer, G., Complex Analytic Geometry. Springer, Berlin-Heidelberg-New York (1976)

    Google Scholar 

  3. Grothendieck, A., Techniques de construction en géométrie analytique, Séminaire H. Cartan, E. N. S., Paris (1960/61)

    Google Scholar 

  4. Kaup, B., Äquivalenzrelationen auf allgeneinen komplexen Räumen, Schr. Math. Inst. Univ. Münster 39, Münster (1968)

    Google Scholar 

  5. Knorr, K., Schneider, M., Relativexzeptionelle analytische Mengen, Math. Ann.193, 238–254 (1971)

    Google Scholar 

  6. Remmert, R., Reduction of complex spaces, in: Princeton Seminars on Analytic Functions, vol. 1, Sem. I, Princeton, 190–205 (1960); vgl. auch: Sur. les espaces analytiques holomorphiquement séparables et holomorphiquement convexes, C. R. Acad. Sci. Paris243, 118–121 (1956)

    Google Scholar 

  7. Siu, Y.-T., Every Stein subvariety admits a Stein neighborhood, Invent. math.38, 89–100 (1976)

    Google Scholar 

  8. Stein, K., Analytische Zerlegungen komplexer Räume, Math. Ann.132, 63–93 (1956)

    Google Scholar 

  9. Wiegmann, K.-W., Über Quotienten holomorph-konvexer komplexer Räume, Math. Z.97, 251–258 (1967)

    Google Scholar 

  10. Wiegmann, K.-W., Strukturen auf Quotienten komptexer Räume, Comm. Math. Helv.44, 93–116 (1969)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, der Universität Duisburg, Lotharstraße 65, D-4100, Duisburg 1

    Kurt Retter

Authors
  1. Kurt Retter
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Retter, K. Relative komplexe quotienten. Manuscripta Math 34, 279–291 (1981). https://doi.org/10.1007/BF01165541

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01165541

Search

Navigation