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  "body": "\n## Summary\n\nIn algebraic geometry, a ruled surface is a smooth projective [[algebraic surface|KFTECAATKG]] that maps onto a curve with every fibre a projective line.\nSo it is a family of lines parametrized by a curve, the algebraic analogue of a surface swept out by a moving line.\nRuled surfaces, together with the projective plane, are the minimal surfaces of Kodaira dimension $-\\infty$.\nThey play a basic role in the classification of surfaces.\n\n## Explanations\n\n### L1 human\n\nImagine a curve, and attach to each of its points a copy of the projective line, varying smoothly.\nThe result is a surface ruled by these lines.\nThe simplest example is the product of a curve with a line.\nThe Hirzebruch surfaces are ruled surfaces over the projective line that are twisted versions of $\\mathbb{P}^1 \\times \\mathbb{P}^1$.\n",
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