The multiplicity of isolated two-dimensional hypersurface singularities

Laufer, Henry B.

doi:10.1090/S0002-9947-1987-0891631-1

The multiplicity of isolated two-dimensional hypersurface singularities
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by Henry B. Laufer

Trans. Amer. Math. Soc. 302 (1987), 489-496

DOI: https://doi.org/10.1090/S0002-9947-1987-0891631-1

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Abstract:

Consider an isolated two-dimensional complex analytic hypersurface singularity $(V,p)$. A relation is given between the abstract topology of $(V,p)$ and the multiplicity of $(V,p)$, yielding an upper bound for the multiplicity. This relation is a necessary condition for a Gorenstein singularity to be a hypersurface.

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