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  "body": "\n## Summary\n\nFujiki class $\\mathcal{C}$ is the class of compact complex manifolds that are bimeromorphic to compact [[Kähler manifolds|X60JG9AEQJ]].\nIt contains all compact Kähler manifolds and all [[Moishezon manifolds|8ZW9P9JRQD]].\nUnlike the Kähler property, membership in class $\\mathcal{C}$ is invariant under bimeromorphic maps and under images of holomorphic maps.\nManifolds in class $\\mathcal{C}$ keep much of the topology of Kähler manifolds: their cohomology has a Hodge decomposition, and their odd Betti numbers are even.\n\n## Explanations\n\n### L1 human\n\nKähler manifolds are compact complex manifolds with a particularly nice kind of metric.\nBlowing up or down, or other birational changes, can destroy that metric, even though the manifold stays almost the same.\nClass $\\mathcal{C}$ is the bigger class one gets by allowing such changes.\nIt is the natural home for results about Kähler manifolds that only depend on the manifold up to birational change.\n",
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