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  "body": "\n## Summary\n\nA K3 surface is a smooth projective [[algebraic surface|KFTECAATKG]], or more generally a compact complex surface, with trivial canonical bundle and no holomorphic $1$-forms.\nK3 surfaces are the two-dimensional [[Calabi–Yau manifolds|STYAB4PFDW]], the surface analogue of elliptic curves.\nAll complex K3 surfaces are diffeomorphic to each other and simply connected, with second Betti number $22$.\nThey are central in the classification of surfaces, in arithmetic geometry and in string theory.\n\n## Explanations\n\n### L1 human\n\nThe simplest K3 surface is a smooth surface of degree $4$ in projective three-space, such as $x^4 + y^4 + z^4 + w^4 = 0$.\nIts canonical bundle is trivial, which means that it carries a nowhere vanishing holomorphic $2$-form, a kind of volume form.\nThis makes K3 surfaces flat in an averaged sense, between the positively curved rational surfaces and the negatively curved surfaces of general type.\n",
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