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 , 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 with nonsingular normalization are locally algebraic.

**[1]**William A. Adkins, Aldo Andreotti, and J. V. Leahy,*An analogue of Oka’s theorem for weakly normal complex spaces*, Pacific J. Math.**68**(1977), no. 2, 297–301. MR**0463484****[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]**Raghavan Narasimhan,*Introduction to the theory of analytic spaces*, Lecture Notes in Mathematics, No. 25, Springer-Verlag, Berlin-New York, 1966. MR**0217337****[6]**Peter Orlik,*The multiplicity of a holomorphic map at an isolated critical point*, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 405–474. MR**0480517****[7]**Pierre Samuel,*Algébricité de certains points singuliers algébroïdes*, J. Math. Pures Appl. (9)**35**(1956), 1–6 (French). MR**0075668**

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0572298-8

Article copyright:
© Copyright 1980
American Mathematical Society