On irreducible components of a Weierstrass-type variety

Romuald A. Janik

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 2, page 169-178
  • ISSN: 0066-2216

Abstract

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We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.

How to cite

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Romuald A. Janik. "On irreducible components of a Weierstrass-type variety." Annales Polonici Mathematici 67.2 (1997): 169-178. <http://eudml.org/doc/270773>.

@article{RomualdA1997,
abstract = {We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.},
author = {Romuald A. Janik},
journal = {Annales Polonici Mathematici},
keywords = {branched covering; Weierstrass-type variety; Galois theory; components of a Weierstrass-type variety; algebraic variety; Nash variety; analytic variety},
language = {eng},
number = {2},
pages = {169-178},
title = {On irreducible components of a Weierstrass-type variety},
url = {http://eudml.org/doc/270773},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Romuald A. Janik
TI - On irreducible components of a Weierstrass-type variety
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 169
EP - 178
AB - We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.
LA - eng
KW - branched covering; Weierstrass-type variety; Galois theory; components of a Weierstrass-type variety; algebraic variety; Nash variety; analytic variety
UR - http://eudml.org/doc/270773
ER -

References

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  1. [1] S. Balcerzyk and T. Józefiak, Commutative Noetherian and Krull Rings, PWN, Warszawa, and Ellis Horwood, Chichester, 1989. 
  2. [2] N. Jacobson, Lectures in Abstract Algebra, Vol. III, Grad. Texts in Math. 32, Springer, 1964. Zbl0124.27002
  3. [3] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, 1991. Zbl0747.32001
  4. [4] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, New York, 1982. Zbl0471.32008
  5. [5] P. Tworzewski, Intersections of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa 17 (1990), 227-271. Zbl0717.32006
  6. [6] H. Whitney, Complex Analytic Varieties, Addison-Wesley, 1972. Zbl0265.32008

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