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1987•Transactions of the American Mathematical SocietyRequires access

The Multiplicity of Isolated Two-Dimensional Hypersurface Singularities

Henry B. Laufer

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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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What this paper is about

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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Available 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.

Key concepts: Hypersurface, Multiplicity (mathematics), Mathematics, Gravitational singularity, Singularity, Isolated singularity, Pure mathematics, Singularity theory

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