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Zeta-function of the monodromy for complete intersection singularities

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The results of A. N. Varchenko regarding the zeta-function of the monodromy operator for a singular point of a hypersurface are generalized to the case of a complete intersection singularity.

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Literature cited

  1. 1.

    H. Busemann, Convex Surfaces, Interscience, New York (1958).

  2. 2.

    A. N. Kirillov, “A formula for the computation of the integral cohomology of the knot of an isolated singularity of a hypersurface,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,100, 106–112 (1980).

  3. 3.

    M. Giusti, “Sur les singularités isolées d'intersections complètes quasihomogènes,” Ann. Inst. Fourier,27, 163–192 (1977).

  4. 4.

    G. Greuel and H. Hamm, “Invarianten quasihomogener vollständiger Durchschnitte,” Invent. Math.,49, 67–86 (1978).

  5. 5.

    H. Hamm, “Lokale topologische Eigenschaften komplexer Räume,” Math. Ann.,191, 235–252 (1971).

  6. 6.

    A. G. Kouchnirenko, “Polyèdres de Newton et nombres de Milnor,” Invent. Math.,32, 1–32 (1976).

  7. 7.

    R. C. Randell, “The homology of generalized Brieskorn manifolds,” Topology,14, 347–355 (1975).

  8. 8.

    R. Randell, “The Milnor number of some isolated complete intersection singularities with C*-action,” Proc. Am. Math. Soc.,72, 375–380 (1978).

  9. 9.

    A. N. Varchenko, “Zeta-function of monodromy and Newton's diagram,” Invent. Math.,37, 253–262 (1976).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 112–120, 1981.

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Kirillov, A.N. Zeta-function of the monodromy for complete intersection singularities. J Math Sci 25, 1051–1057 (1984). https://doi.org/10.1007/BF01680828

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  • Singular Point
  • Complete Intersection
  • Intersection Singularity
  • Monodromy Operator
  • Complete Intersection Singularity