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Almost analytic local algebraicity of analytic sets and functions

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References

  1. Akbulut, S., King, H.: Submanifolds and homology of nonsingular real algebraic varieties. Am. J. Math.107, 45–83 (1985)

    Google Scholar 

  2. Artin, M.: Algebraic approximation of structures over complete local rings. Publ. I.H.E.S.36, 23–58 (1969)

    Google Scholar 

  3. Bochnak, J., Kucharz, W., Shiota, M.: On algebraicity of global analytic sets and functions. Invent. Math.70, 115–156 (1982)

    Google Scholar 

  4. Bochnak, J., Kucharz, W.: Local algebraicity of analytic sets. J. Reine Angew. Math.352, 1–14 (1984)

    Google Scholar 

  5. Bochnak, J.: Algebraicity versus analyticity. Rocky Mountain J. of Math.14, 863–880 (1934)

    Google Scholar 

  6. Cerveau, D., Mattei, J.G.: Formes intégrables holomorphes singulières. Astérisque97 (1982)

  7. Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero I, II. Ann. of Math.79, 109–326 (1964)

    Google Scholar 

  8. Kucharz, W.: Power series and smooth functios equivalent to a polynomial. Proc. Am. Math. Soc.98, 527–533 (1986)

    Google Scholar 

  9. Kuo, T.C., Ward, J.N.: A theorem on almost analytic equisingularity. J. Math. Soc. Japan33, 471–488 (1981)

    Google Scholar 

  10. Kuo, T.C.: The modified analytic trivialization of singularities. J. Math. Soc. Japan32, 605–614 (1980)

    Google Scholar 

  11. Kuo, T.C.: Une classification des singularités isolées. C.R. Acad. Sci. Paris,288, 809–812 (1979)

    Google Scholar 

  12. Kuo, T.C.: On classification of real singularities. Invent. Math.82, 257–262 (1985)

    Google Scholar 

  13. Serre, J.P.: Faisceaux algébriques cohérents. Ann. of Math.61, 197–278 (1956)

    Google Scholar 

  14. Shiota, M.: Equivalence of differentiable mappings and analytic mappings. Publ. I.H.E.S.54, 37–122 (1981)

    Google Scholar 

  15. Tougeron, J.Cl.: Idéaux de fonctions differentiables. I. Ann. Inst. Fourier18, 177–240 (1968)

    Google Scholar 

  16. Tougeron, J.Cl.:G-stabilité des germes d'applications différentiables. Preprint, Université de Rennes (1971)

  17. Tougeron, J.Cl.: Idéaux de fonctions différentiables. Ergebnisse der Math., Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  18. Tougeron, J.Cl.: Solution d'un systéme d'équations analytiques réelles et applications. Ann. Inst. Fourier26, 109–135 (1976)

    Google Scholar 

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Dedicated to Professor Tzee-Char Kuo

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Buchner, M.A., Kucharz, W. Almost analytic local algebraicity of analytic sets and functions. Math Z 196, 65–74 (1987). https://doi.org/10.1007/BF01179268

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