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  "body": "\n## Summary\n\nAn isolated hypersurface singularity is the germ at a point of the zero set of a holomorphic function $f$ of $n + 1$ variables, see the [[definition|4KAWK0FD4V]].\nThe gradient of $f$ vanishes at the point but nowhere else nearby.\nIt is the basic object of the local theory of [[singularities|42V5XGZS4F]] of complex spaces.\nIts topology is described by the [[Milnor fibration|KTFG1S2SMG]], the [[link|C831AN3RFM]] and the [[Milnor number|1ZE51P7GRQ]].\nIt is a special kind of [[singular point|ZW5A88PCPK]] of a [[complex analytic variety|GB7M582M5Y]].\n\n## Explanations\n\n### L1 human\n\nA hypersurface in $\\C^{n+1}$ is the set where one holomorphic function is zero.\nAt most points it is smooth, like a curved sheet.\nAt an isolated singularity it has a single bad point, such as the tip of a cone, while every nearby point is smooth.\nThe cone $z_0^2 + z_1^2 + z_2^2 = 0$ in $\\C^3$ is the simplest example: its only singular point is the origin.\n",
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