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  "body": "\n## Summary\n\nA del Pezzo surface is a smooth projective [[algebraic surface|KFTECAATKG]] whose anticanonical divisor is ample.\nThese are exactly the [[Fano varieties|FMHA649HJ9]] of dimension two.\nOver an algebraically closed field they are $\\mathbb{P}^1 \\times \\mathbb{P}^1$ and the blow-ups of the plane in at most eight points in general position.\nSo they are [[rational surfaces|55A4A53TRF]].\nTheir degree $K^2$ runs from $1$ to $9$, and the curves of self-intersection $-1$ on them are governed by root systems of type $E$.\n\n## Explanations\n\n### L1 human\n\nDel Pezzo surfaces are the most positively curved surfaces in the algebraic sense.\nOne gets them by taking the projective plane and blowing up a few points in sufficiently general position.\nEach blown-up point is replaced by a line, and new lines appear from the lines and conics through the chosen points.\nThe smooth cubic surfaces in space, with their $27$ lines, are the del Pezzo surfaces of degree $3$.\n",
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