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  "body": "\n## Summary\n\nThe Kodaira dimension of a smooth projective variety measures how fast the spaces of sections of the powers of its [[canonical bundle|W05VYY4HBR]] grow.\nIt takes one of the values $-\\infty, 0, 1, \\dots, n$, where $n$ is the dimension of the variety.\nIt is a birational invariant, and it is the first coarse invariant in the classification of varieties, as in the [[Enriques–Kodaira classification|1GVF19KFAK]] of surfaces.\nVarieties of maximal Kodaira dimension are said to be of general type.\n\n## Explanations\n\n### L1 human\n\nThe canonical bundle of a variety is built from its top-degree differential forms.\nCount how many independent sections the $m$-th power of this bundle has, and watch how this number grows with $m$.\nIf it is always zero, the Kodaira dimension is $-\\infty$; if it grows like $m^\\kappa$, the Kodaira dimension is $\\kappa$.\nFor curves, this gives three classes: the projective line has $-\\infty$, elliptic curves have $0$, and curves of genus at least $2$ have $1$.\nThese three classes match the three geometries: spherical, flat and hyperbolic.\n",
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