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Local algebraicity of some analytic hypersurface

Author: William A. Adkins
Journal: Proc. Amer. Math. Soc. 79 (1980), 546-548
MSC: Primary 32C40; Secondary 14B05
MathSciNet review: 572298
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Abstract: It is proved that an analytic hypersurface germ $ (X,0) \subseteq ({{\mathbf{C}}^{n + 1}},0)$, with nonsingular normalization, whose only singularities outside the origin are normal crossings of two n-manifolds is isomorphic to a germ of an algebraic variety at 0. As a corollary we find that weakly normal surfaces $ V \subseteq {{\mathbf{C}}^3}$ with nonsingular normalization are locally algebraic.

References [Enhancements On Off] (What's this?)

  • [1] W. A. Adkins, A. Andreotti and J. V. Leahy, An analogue of Oka's theorem for weakly normal complex spaces, Pacific J. Math. 68 (1977), 297-301. MR 0463484 (57:3433)
  • [2] -, Weakly normal complex spaces (to appear).
  • [3] T. Gaffney, Properties of finitely determined germs, Thesis, Brandeis Univ., 1975.
  • [4] J. N. Mather, Finitely determined map germs, Publ. Math. Inst. Hautes Étude Sci. 35 (1968), 127-156.
  • [5] R. Narasimhan, Introduction to the theory of analytic spaces, Lecture Notes in Math., vol. 25, Springer-Verlag, Berlin, 1966. MR 0217337 (36:428)
  • [6] P. Orlik, The multiplicity of a holomorphic map at an isolated critical point, Real and Complex Singularities (Oslo, 1976), Sijthoff & Noordhoff, Amsterdam, 1978, pp. 405-474. MR 0480517 (58:677)
  • [7] P. Samuel, Algébricité de certains points singuliers algébroides, J. Math. Pures Appl. 35 (1956), 1-6. MR 0075668 (17:788b)

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