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  "body": "\n## Summary\n\nA generic point of a closed set $Z$ in a topological space is a point whose closure is all of $Z$.\nIn a [[scheme|5A35TYZD02]], every irreducible closed subset has exactly one generic point.\nGeneric points let one speak of a property holding \"at a general point\" of a variety.\nFunctions at the generic point form the function field.\n\n## Explanations\n\n### L1 human\n\nIn classical geometry, every point of a curve is a single spot on it.\nA scheme adds one more point for the whole curve, which lies \"everywhere on it at once\".\nIn $\\operatorname{Spec} \\C[x, y]$, the prime ideal $(y - x^2)$ is such a point: its closure contains all the points $(x - a, y - a^2)$ of the parabola.\nSimilarly, $(0)$ is the generic point of $\\operatorname{Spec} \\Z$, and its closure is the whole space.\nA statement true at the generic point is often true on a dense open set.\n",
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