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  "body": "\n## Summary\n\nA Fano variety is a smooth projective variety whose anticanonical bundle is ample.\nFano varieties are the positively curved end of the classification of varieties, opposite to varieties of general type.\nThey appear as the general fibres of Mori fibre spaces in the [[minimal model program|Q8CTDCZH01]].\nIn dimension $2$ they are the del Pezzo surfaces.\n\n## Explanations\n\n### L1 human\n\nThe canonical bundle measures how a variety curves, and a Fano variety curves positively in every direction, like a sphere.\nProjective space is the main example.\nA smooth hypersurface of degree $d$ in $\\mathbb{P}^n$ is Fano exactly when $d \\le n$: a smooth conic or a smooth cubic surface is Fano, but a smooth plane cubic is not.\nFano varieties have many rational curves, which makes them close to rational varieties.\n",
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