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Remark on Irreducible Factorizations of Polynomials in Several Variables*

Published online by Cambridge University Press:  20 November 2018

Leiba Rodman
Leiba Rodman*
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, 2500 University Drive N.W.Calgary, Alberta T2N 1N4, Canada
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Abstract

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It is proved that a polynomial on several complex variables, whose coefficients depend analytically on a parameter ε, admits a factorization which is irreducible for every value of the parameter, with the possible exception of an analytic set of points. Moreover, the coefficients of the irreducible factors can be chosen to depend analytically on ε in a neighborhood of every point not belonging to this analytic set.

Keywords

30A0632A05.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 493 - 496
Copyright
Copyright © Canadian Mathematical Society 1981

Footnotes

*

Partially supported by NSERC.

References

1. Shafarevich, I. R., Basic Algebraic Geometry, Springer-Verlag, New York-Heidelberg-Berlin, 1974.Google Scholar
2. Gunning, R. C. and Rossi, H., Analytic functions of several complex variables, Prentice-Hall, Englewood Cliffs, N.J., 1965.Google Scholar