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  "body": "\n## Definition\n\nLet $X$ be a compact, connected [[complex manifold|JSGWAN2RJV]].\nThen $X$ is *in Fujiki class $\\mathcal{C}$* if there are a compact [[Kähler manifold|X60JG9AEQJ]] $Y$ and a compact complex manifold $Z$ with the following property.\nThere are [[modifications|SB3MY7XQM9]] $p \\colon Z \\to X$ and $q \\colon Z \\to Y$.\nHere a surjective holomorphic map $f \\colon Z \\to V$ is a *modification* if it satisfies the following condition.\nThere is a nowhere dense analytic subset $A \\subset V$ such that $f^{-1}(A)$ is nowhere dense in $Z$ and $f$ maps $Z \\setminus f^{-1}(A)$ biholomorphically onto $V \\setminus A$.\nIn other words, $X$ is bimeromorphic to a compact Kähler manifold.\n\n## Remarks\n\nFujiki's original definition, for reduced compact complex spaces, asks that $X$ be the image of a compact Kähler space under a meromorphic map.\nBy a theorem of Varouchas, for compact complex manifolds this is equivalent to the definition above.\n\nExample: every compact Kähler manifold $X$ is in class $\\mathcal{C}$, with $Y = Z = X$ and $p = q = \\id$.\nEvery [[Moishezon manifold|8ZW9P9JRQD]] is in class $\\mathcal{C}$, since it is bimeromorphic to a projective manifold, which is Kähler.\n\nNon-example: a [[Hopf surface|PNFNGBXRM3]] is not in class $\\mathcal{C}$.\nManifolds in class $\\mathcal{C}$ have even odd Betti numbers, as compact Kähler manifolds do, while a Hopf surface has $b_1 = 1$.\n",
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