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  "body": "\n## Summary\n\nA reduced complex space is a [[complex analytic space|HXSZA44J5J]] whose structure sheaf has no nonzero nilpotent germs.\nOn such a space, a function is determined by its values at points, so the structure sheaf is a sheaf of genuine complex-valued functions.\nReduced complex spaces are the same as complex analytic varieties with their sheaves of holomorphic functions.\nEvery complex space has a reduction, a reduced complex space with the same underlying topological space.\n\n## Explanations\n\n### L1 human\n\nA complex space may carry extra infinitesimal information, such as the double point given by $z^2 = 0$, where $z$ is a nonzero function that vanishes at the only point.\nA reduced complex space has none of this extra information.\nIts functions are ordinary functions, and a function that is zero at every point is zero.\nThe cross $\\set{z_1 z_2 = 0}$ in $\\C^2$ is reduced, while the doubled line $\\set{z_1^2 = 0}$ is not.\n",
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