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  "body": "\n## Summary\n\nA normal complex space is a [[complex analytic space|HXSZA44J5J]] whose local rings are integrally closed domains.\nNormal spaces are [[reduced|831N2Q4GCB]], locally irreducible, and their singular locus has codimension at least $2$.\nOn a normal space, the Riemann extension theorem holds: a function that is holomorphic off the singular locus and locally bounded is holomorphic.\nEvery reduced complex space has a normalization, so normal spaces are a standard first step in the study of singularities.\n\n## Explanations\n\n### L1 human\n\nSingular points come in different degrees of badness.\nAt a normal point, the space does not cross itself and is not pinched like the cusp $z_2^2 = z_1^3$.\nFor example, the cone $\\set{z_1 z_2 = z_3^2}$ in $\\C^3$ is normal, even though its vertex is a singular point.\nA normal curve is the same as a smooth curve, but in higher dimension normal spaces can have singularities.\n",
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