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A reduction theorem for the Zariski multiplicity conjecture

Author: David B. Massey
Journal: Proc. Amer. Math. Soc. 106 (1989), 379-383
MSC: Primary 32B30; Secondary 14B05
MathSciNet review: 949879
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Abstract: We prove that the Zariski multiplicity conjecture for families of hypersurfaces of dimension \ensuremath{ eq}2 with isolated singularities is equivalent to the conjecture for families of hypersurfaces with line singularities.

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  • [G] G. M. Greuel, Constant Milnor number implies constant multiplicity for quasihomogeneous singularities, Manuscripta Math., 56, Fase. 2 (1986), 159-166. MR 850367 (87j:32020)
  • [HL] H. Hamm and D. T. Lê, Un Theoreme de Zariski du type de Lefschetz, Ann. Sci. Ecole Norm. Sup. 6 (1973), 317-366. MR 0401755 (53:5582)
  • [I] I. N. Iomdine, Complex varieties with singularities of dimension one, Sibirsk Mat. Zh. 15 (1974), 1061-1082. MR 0447621 (56:5931)
  • [L$ _{1}$] D. T. Lê, Calcul du nombre de cycle evanouisssant d'une hypersurface complexe, Ann. Inst. Fourier (Grenoble) 23 (1973), 261-270. MR 0330501 (48:8838)
  • [L$ _{2}$] -, Ensembles analytiques complexes avec lieu singulier de dimension un (D'Apres I. N. Iomdine) Seminar on singularities (Paris, 1976/1977), Publ. Math. Univ. Paris VII 7 (1980), 87-95.
  • [L3] -, Topologie des singuarlities des hypersurfaces complexes, Singularities a Cargese in Asterique 7 et 8 (1973), 171-182.
  • [LR] T. Lê and C. P. Ramanujam, The invariance of Milnor's number implies the invariance of the topological type, Amer. J. Math. 98 (1976), 67-78. MR 0399088 (53:2939)
  • [M] D. B. Massey, Families of hypersurfaces with one-dimensional singular setes, Dissertation, Duke University, 1986.
  • [O] D. O'Shea, Topologically trivial deformations of isolated quasihomogeneous hypersurface singularities are equimultiple, Proc. Amer. Math. Soc. 100 (1987), 260-262. MR 902538 (88k:32056)
  • [Z] O. Zariski, Open questions in the theory of singularities, Bull. Amer. Math. Soc. 77 (1971), 481-491. MR 0277533 (43:3266)

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Keywords: Zariski multiplicity conjecture, one-dimensional hypersurface singularities
Article copyright: © Copyright 1989 American Mathematical Society

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