Advertisement

Monatshefte für Mathematik

, Volume 89, Issue 4, pp 323–340 | Cite as

Über allgemeine Hyperflächenschnitte einer algebraischen Varietät

  • Ngô Viêt Trung
Article
  • 22 Downloads

On general hyperplane sections of an algebraic variety

Abstract

LetV/k be an irreducible algebraic variety over a fieldk in an affinen-space andF u a generic hypersurface defined byu1f1 (X)+...+u r fr(X)=0, whereu1...,ur are indeterminates overk andf1(X), ...,fr(X) are polynomials ink[X1, ...,Xn]. Let (E) be a property which an arbitrary algebraic variety could have, e. g. irreducibility, normality (local or global), ... Then it will be studied under which conditions off1(X), ...,fr(X) (E) may be transfered fromV/k toVF u /k(u) (and conversely).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    Cuong, N. T., P. Schenzel, undN. V. Trung: Verallgemeinerte Cohen-Macaulay-Moduln. Math. Nachr.85, 57–73 (1978).Google Scholar
  2. [2]
    Hochster, M.: Properties of noetherian rings stable under general grade reduction. Arch. Math.24, 393–396 (1973).Google Scholar
  3. [3]
    Kuan, W.-E.: A note on a generic hyperplane section of an algebraic variety. Canad. J. Math.22, 1047–1054 (1970).Google Scholar
  4. [4]
    Kuan, W.-E.: On the hyperplane section through a rational point of an algebraic variety. Pacific J. Math.36, 393–405 (1971).Google Scholar
  5. [5]
    Kuan, W.-E.: Some results on normality of a graded ring. Preprint.Google Scholar
  6. [6]
    Lang, S.: Introduction to algebraic Geometry. New York: Interscience 1964.Google Scholar
  7. [7]
    Nagata, M.: Local Rings. New York: Interscience. 1962.Google Scholar
  8. [8]
    Noether, E.: Ein algebraisches Kriterium für absolute Irreduzibilität. Math. Ann.85, 26–33 (1922).Google Scholar
  9. [9]
    Reich, L.: Über unirationale Scharen auf algebraischen Mannigfaltigkeiten. Math. Ann.167, 259–270 (1966).Google Scholar
  10. [10]
    Seidenberg, A.: The hyperplane section, of normal varieties. Trans. Amer. Math. Soc.69, 357–386 (1950).Google Scholar
  11. [11]
    Seidenberg, A.: The hyperplane section of arithmetically normal varieties. Amer. J. Math.94, 609–630 (1972).Google Scholar
  12. [12]
    Stückrad, J., undW. Vogel: Eine Verallgemeinerung der Cohen-Macaulay-Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie. J. Math. Kyoto Univ.13, 513–528 (1973).Google Scholar
  13. [13]
    Trung, N. V.: Über die Übertragung der Ringeigenschaften zwischenR undR[u]/(F). Math. Nachr. (Im Druck).Google Scholar
  14. [14]
    Trung, N. V.: Spezialisierungen allgemeiner Hyperflächenschnitte und Anwendungen. Preprint.Google Scholar
  15. [15]
    Zariski, O.: the theorem of Bertini on the variable points of a linear system of varieties. Trans. Amer. Math. Soc.56, 130–140 (1946).Google Scholar
  16. [16]
    Zariski, O., undP. Samuel: Commutative Algebra I. New York-Heidelberg-Berlin: Springer. 1975.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Ngô Viêt Trung
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

Personalised recommendations