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Equisingularity of Analytically Constructible Sets

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Complex Analysis

Part of the book series: Aspects of Mathematics ((ASMA,volume 1))

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Abstract

In this note(*) we study general properties of analytically constructible sets and their connections with constructible sets in the sense of C. Chevalley. After that we give certain description of equisingular stratifications of the sets. The author is very indebted to Professor Stanisław Łojasiewicz for teaching him analytic geometry in the presented spirit.

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References

  1. M. Artin, Grothendieck topologies, Harvard Math. Dept. Lecture Notes (1962).

    Google Scholar 

  2. H. Cartan, C. Chevalley, Géométrie Algébrique, Séminaire Cartan-Chevalley, Secrétariat Math., Paris (1955/1956).

    Google Scholar 

  3. H. Delfs, M. Knebusch, Locally semialgebraic spaces, Springer Lecture Notes in Mathematics 1173.

    Google Scholar 

  4. H. Grauert, On Levi’s problem and the imbedding of real analytic manifolds, Ann. of Math. 68, (1958), 460–472.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Grauert R. Remmert, Coherent Analytic Sheaves, Springer-Verlag, Heidelberg (1986).

    Google Scholar 

  6. A. Grothendieck, J. Dieudonné, EGA III, Publ. Math. IHES 11 (1961).

    Google Scholar 

  7. Z. Hajto, Whitney (6)-regularity for analytically constructible sets, Algebraic geometry, Proc. Conf., Berlin 1985, Teubner-Texte Math. 92, (1986) (117–122).

    MathSciNet  Google Scholar 

  8. S. Łojasiewicz, Ensembles semi-analytiques, I.H.E.S., Bures-sur-Yvette 1965.

    Google Scholar 

  9. S. Łojasiewicz, Wstep do geometrii analitycznej zespolonej, PWN Warszawa (1988) (english version in print by Birkhäuser Verlag).

    Google Scholar 

  10. T. Mostowski, Lipschitz equisingularity, Dissertationes Math. 243 (1985).

    Google Scholar 

  11. A. Płoski, Multiplicity and the Łojasiewicz exponent, Banach Center Publications, volume 20 (353-364).

    Google Scholar 

  12. B. Teissier, Variétés polaires II, Springer Lecture Notes in Mathematics 961 (314-491).

    Google Scholar 

  13. D. Trotman, Thèse, Orsay 1980.

    Google Scholar 

  14. R. Thom, Ensembles et morphismes stratifiés, Bull. A.M.S., 75 (1969) (240–284).

    Article  MathSciNet  MATH  Google Scholar 

  15. C.T.C. Wall, Regular stratifications, Springer Lecture Notes in Mathematics 468 (332–344).

    Google Scholar 

  16. H. Whitney, Complex Analytic Varieties. Reading Mass., Addison-Wesley 1972.

    Google Scholar 

  17. H. Whitney, Tangents to an analytic variety, Ann. of Math. 81, (1964).

    Google Scholar 

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© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Hajto, Z. (1991). Equisingularity of Analytically Constructible Sets. In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_23

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  • DOI: https://doi.org/10.1007/978-3-322-86856-5_23

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-86858-9

  • Online ISBN: 978-3-322-86856-5

  • eBook Packages: Springer Book Archive

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