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  "body": "\n## Summary\n\nA line bundle on a proper variety is nef, short for numerically effective or numerically eventually free, when its degree on every curve is nonnegative.\nNef line bundles are the limits of [[ample line bundles|RRK8P6TXG2]]: on a projective variety, the nef cone is the closure of the ample cone.\nNefness is a numerical condition, so it depends only on intersection numbers with curves.\nIt is central in the [[minimal model program|Q8CTDCZH01]], where a minimal model is a variety with mild (terminal) singularities whose canonical divisor is nef.\n\n## Explanations\n\n### L1 human\n\nEach line bundle on a variety has a degree on each curve inside the variety, an integer that counts zeros minus poles of a section restricted to the curve.\nAn ample bundle has positive degree on every curve.\nA nef bundle is allowed degree zero on some curves, but never negative degree.\nOn the product $\\mathbb{P}^1 \\times \\mathbb{P}^1$, pulling back $\\mathcal{O}(1)$ from the first factor gives a nef bundle.\nIt has degree $1$ on the curves $\\mathbb{P}^1 \\times \\set{q}$ and degree $0$ on the curves $\\set{p} \\times \\mathbb{P}^1$, so it is nef but not ample.\n",
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  "msc": [
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  "name": "Nef line bundle",
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