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  "body": "\n## Summary\n\nA quasi-projective variety is an open subset of a projective variety, with the induced Zariski topology.\nThe class contains both the affine varieties and the projective varieties, and it is closed under taking open and closed subvarieties.\nIn classical algebraic geometry, the quasi-projective varieties are exactly the varieties one works with.\n\n## Explanations\n\n### L1 human\n\nStart with a projective variety and remove a closed piece of it, defined by some equations.\nWhat is left is a quasi-projective variety.\nRemoving the line at infinity from the projective plane leaves the affine plane, so affine varieties are quasi-projective.\nRemoving a single point from the affine plane leaves a quasi-projective variety that is neither affine nor projective.\n",
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