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  "body": "\n## Summary\n\nNevanlinna theory in several variables is the value distribution theory of holomorphic maps whose source or target has dimension greater than one.\nIts model case is a holomorphic curve $f \\colon \\C \\to \\mathbb{P}^n$, studied against hyperplanes, and more generally holomorphic maps from $\\C^m$ to projective varieties, studied against divisors.\nIt extends the one-variable [[Nevanlinna theory|1EHH63VNAD]], with a characteristic function, counting functions and proximity functions, and first and second main theorems.\nIt is closely tied to [[Kobayashi hyperbolicity|HRPAX8V7HA]] and, through an analogy found by Vojta, to Diophantine approximation.\n\n## Explanations\n\n### L1 human\n\nOne-variable Nevanlinna theory measures how often a meromorphic function on the plane hits each value.\nIn several variables the questions are the same, for maps into higher-dimensional spaces such as projective space.\nFor a curve in $\\mathbb{P}^n$, the role of the values is played by hyperplanes, and one asks how often the curve meets each hyperplane.\nCartan's second main theorem says, roughly, that a curve not contained in any hyperplane cannot avoid too many hyperplanes in general position.\nFor $n = 1$ it gives Picard's theorem: a nonconstant meromorphic function on $\\C$ omits at most two values.\n",
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