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  "body": "\n## Summary\n\nA toric variety is a variety that contains an [[algebraic torus|66FQFAJNS4]] as a dense open subset.\nThe action of the torus on itself must extend to the whole variety.\nNormal toric varieties correspond to combinatorial objects called fans, built from rational polyhedral cones.\nSo geometric questions about them turn into questions about cones and polytopes, such as [[Newton polytopes|CYTTX8KHC8]].\nThey are a standard testing ground for conjectures and constructions in algebraic geometry.\n\n## Explanations\n\n### L1 human\n\nStart with the points $(x, y)$ where both coordinates are nonzero; this is a two-dimensional torus.\nAdding back the coordinate axes gives the plane, and adding a line at infinity gives the projective plane.\nIn each case the torus sits inside as a dense open part, and scaling the coordinates still makes sense on the whole space.\nSuch spaces are toric varieties, and the way they are glued from the torus is recorded by a picture of cones in a lattice.\n",
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