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  "body": "\n## Summary\n\nAn invertible sheaf on a ringed space is a sheaf of modules that is locally isomorphic to the structure sheaf.\nIt is the algebraic version of a line bundle, a family of one-dimensional vector spaces over the points of the space.\nThe name comes from the fact that, on a scheme, such sheaves are exactly the sheaves of modules with an inverse for the tensor product.\nTheir isomorphism classes form the Picard group.\n\n## Explanations\n\n### L1 human\n\nA line bundle attaches a line to each point of a space, and these lines vary smoothly.\nLocally it looks like the space times a line, but globally it can twist, like a Möbius band over a circle.\nAn invertible sheaf records the sections of a line bundle: over small open sets they are just functions, but globally they can be glued with a twist.\nOn projective space, the twisting sheaves $\\mathcal{O}(n)$ are the basic examples, and for $n \\ge 0$ the global sections of $\\mathcal{O}(n)$ are the homogeneous polynomials of degree $n$.\n",
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