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  "body": "\n## Summary\n\nAn ideal sheaf on a ringed space $X$ is a subsheaf of the structure sheaf $\\mathcal{O}_X$ whose sections over each open set form an ideal.\nIt is the sheaf version of an ideal of a ring.\nOn a scheme, quasi-coherent ideal sheaves correspond exactly to closed subschemes, the subscheme being cut out by the functions in the ideal.\n\n## Explanations\n\n### L1 human\n\nAn ideal of a ring of functions is a set of functions closed under addition and under multiplication by any function.\nAn ideal sheaf picks such an ideal on every open set, in a way compatible with restriction.\nThe typical example is the sheaf of functions that vanish on a fixed closed subset, such as a point or a curve.\nThe ideal sheaf then remembers that subset, and even multiplicities, such as functions vanishing to order two at a point.\n",
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