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  "body": "\n## Summary\n\nA projective morphism $X \\to Y$ is a morphism that embeds $X$ as a closed subscheme of a projective space over $Y$.\nIt is the relative form of a projective variety: a family of projective schemes parametrized by $Y$.\nProjective morphisms are proper, and most proper morphisms met in practice are projective.\n\n## Explanations\n\n### L1 human\n\nA projective variety is cut out by homogeneous polynomial equations inside projective space.\nA projective morphism to $Y$ is the same thing with coefficients that vary over $Y$.\nFor example, the equations $y^2 z = x^3 + t x z^2 + z^3$ in $\\mathbb{P}^2$, with a parameter $t$, describe a family of plane cubic curves over the $t$-line.\nThe map that sends each point of the family to its value of $t$ is projective.\n",
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