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  "body": "\n## Summary\n\nA meromorphic function of several variables is locally a quotient of two [[holomorphic functions|507C34W0ZT]] on an open set of $\\C^n$.\nThe denominator must not be identically zero.\nIt extends the one-variable notion of a [[meromorphic function|0ZZ7ZYDR8W]].\nA new feature for $n \\ge 2$ is the presence of points of indeterminacy, where the function has no value at all, not even $\\infty$.\nMeromorphic functions are the natural analogue of rational functions on complex manifolds and analytic spaces.\n\n## Explanations\n\n### L1 human\n\nRational functions such as $z_1 / z_2$ are the simplest meromorphic functions on $\\C^2$.\nThis function has poles along the line $z_2 = 0$, except at the origin.\nNear the origin it takes every complex value: along the line $z_1 = c z_2$ it is constantly equal to $c$.\nSo at the origin it cannot be given any value, finite or infinite; the origin is a point of indeterminacy.\nIn one variable this never happens, because poles are isolated points where the function tends to $\\infty$.\n",
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