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Transactions of the American Mathematical Society

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The Cartesian product structure and $ C\sp{\infty }$ equivalances of singularities

Author: Robert Ephraim
Journal: Trans. Amer. Math. Soc. 224 (1976), 299-311
MSC: Primary 32C40; Secondary 32B10
MathSciNet review: 0422676
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Abstract: In this paper the cartesian product structure of complex analytic singularities is studied. A singularity is called indecomposable if it cannot be written as the cartesian product of two singularities of lower dimension. It is shown that there is an essentially unique way to write any reduced irreducible singularity as a cartesian product of indecomposable singularities. This result is applied to give an explicit description of the set of reduced irreducible complex singularities having a given underlying real analytic structure.

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  • [1] Norbert A’Campo, Le nombre de Lefschetz d’une monodromie, Nederl. Akad. Wetensch. Proc. Ser. A 76 = Indag. Math. 35 (1973), 113–118 (French). MR 0320364
  • [2] Thomas Bloom, 𝐶¹ functions on a complex analytic variety, Duke Math. J. 36 (1969), 283–296. MR 0241688
  • [3] Henri Cartan, Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957), 77–99 (French). MR 0094830
  • [4] Robert Ephraim, 𝐶^{∞} and analytic equivalence of singularities, Rice Univ. Studies 59 (1973), no. 1, 11–32. Complex analysis, 1972 (Proc. Conf., Rice Univ., Houston, Tex., 1972), Vol. I: Geometry of singularities. MR 0330497
  • [5] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
  • [6] John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
  • [7] David Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. 9 (1961), 5–22. MR 0153682
  • [8] Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. MR 0155856
  • [9] Raghavan Narasimhan, Introduction to the theory of analytic spaces, Lecture Notes in Mathematics, No. 25, Springer-Verlag, Berlin-New York, 1966. MR 0217337
  • [10] Hugo Rossi, Vector fields on analytic spaces, Ann. of Math. (2) 78 (1963), 455–467. MR 0162973
  • [11] Hassler Whitney, Local properties of analytic varieties, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N. J., 1965, pp. 205–244. MR 0188486

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Keywords: Reduced singularity, irreducible singularity, cartesian product, underlying real analytic structure, complexification, complex conjugate, real analytic isomorphism, $ {C^\infty }$ isomorphism
Article copyright: © Copyright 1976 American Mathematical Society