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  "body": "\n## Summary\n\nA Moishezon manifold is a compact connected [[complex manifold|JSGWAN2RJV]] with as many independent meromorphic functions as its dimension.\nIn other words, its [[algebraic dimension|F0GF0JEZTG]] equals its dimension.\nEvery projective manifold is Moishezon.\nMoishezon proved that every Moishezon manifold becomes projective after finitely many blow-ups along smooth centres.\nHe also proved that a Moishezon manifold is projective if and only if it is [[Kähler|X60JG9AEQJ]].\nSo Moishezon manifolds are the compact complex manifolds closest to algebraic varieties; they are the manifolds that correspond to proper algebraic spaces.\n\n## Explanations\n\n### L1 human\n\nA Moishezon manifold carries enough meromorphic functions to serve as coordinates almost everywhere.\nProjective varieties, the spaces cut out by polynomial equations in projective space, are the main examples.\nThere are also Moishezon manifolds that are not projective, first found by Hironaka in dimension $3$, but they differ from projective ones only by a birational change.\nIn dimension $2$ every Moishezon manifold is projective.\n",
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