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  "body": "\n## Summary\n\nAn affine variety is an irreducible algebraic set in affine space $k^n$ over an algebraically closed field $k$.\nAffine varieties are the local building blocks of all algebraic varieties.\nAn affine variety corresponds to a prime ideal of the polynomial ring, and it is determined up to isomorphism by its coordinate ring.\nSome authors drop the irreducibility condition and call every algebraic set an affine variety.\n\n## Explanations\n\n### L1 human\n\nAn affine variety is the solution set of polynomial equations that cannot be broken into smaller solution sets.\nThe parabola $y = x^2$ in the plane is one: it is a single piece.\nThe set $xy = 0$ is not, since it splits into the two axes.\nLines, planes, smooth conics and the whole space $k^n$ are all affine varieties.\n",
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