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  "body": "\n## Summary\n\nA rational map from a variety $X$ to a variety $Y$ is a morphism defined on some nonempty open subset of $X$.\nTwo such morphisms give the same rational map when they agree on a common open subset.\nIt is written $X \\dashrightarrow Y$, because it may fail to be defined at some points.\nRational maps are the maps of birational geometry, which studies varieties up to changes on lower-dimensional subsets.\n\n## Explanations\n\n### L1 human\n\nSome natural maps are given by formulas with denominators, so they are undefined where a denominator vanishes.\nThe projection of the plane from the origin onto the line of directions, $(x, y) \\mapsto [x : y]$, is defined everywhere except at the origin.\nA rational map keeps such a formula and simply forgets the bad points.\nBecause varieties are irreducible, the open set where the map is defined is dense, so the formula determines the map.\n",
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