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Elementary Structure of Real Algebraic Varieties

  • Hassler Whitney
Part of the Contemporary Mathematicians book series (CM)

Abstract

A real (or complex) algebraic variety V is a point set in real n-space R n (or complex n-space C n ) which is the set of common zeros of a set of polynomials. The general properties of a real V as a point set have not been the subject of much study recently (but see for instance [2], [3] and [4]); attention has turned more to the complex case, the complex projective case, and especially the abstract algebraic theory. Facts about the real case are sometimes needed in the applications; proofs are commonly very difficult to locate.

Keywords

Variety Versus Algebraic Variety Constant Dimension Splitting Process Real Algebraic Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. [1]
    W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry, volume II, University Press, Cambridge, 1952.Google Scholar
  2. [2]
    S. Lefschetz, L’Analysis situs et la géométrie algébrique, Paris, 1924 and 1950.Google Scholar
  3. [3]
    J. Nash,Real algebraic manifolds,Ann. of Math., 56 (1952), pp. 405–421.CrossRefGoogle Scholar
  4. [4]
    O. A. Oleinik,Estimates of the Betti numbers of real algebraic hy per surfaces,Rec. Math. (Mat. Sbornik) N.S., 28 (70), 1951, pp. 635–640.Google Scholar
  5. [5]
    B. L. Van Der Waerden, Algebra, volume II ( third ed. ), Springer, Berlin, 1955.Google Scholar
  6. [6]
    B. L. Van Der Waerden, Einführung in die algebraische Geometrie, Springer, Berlin, 1939 ( Dover, NewYork, 1945).Google Scholar

Copyright information

© Birkhäuser Boston 1992

Authors and Affiliations

  • Hassler Whitney

There are no affiliations available

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