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  "body": "\n## Summary\n\nIntersection theory studies how subvarieties of an algebraic variety meet, and assigns numbers and classes to their intersections.\nIts central object is the Chow ring of a smooth variety, made of the [[Chow groups|EBEF6PEK4N]].\nIts product sends two cycle classes to the class of their intersection, counted with [[intersection multiplicity|GPQF9GK4T9]].\nIt gives a rigorous form to classical enumerative geometry, including [[Bézout's theorem|KWNVF194D8]] and [[Schubert calculus|FWGHMADJR4]].\nIt is also the home of [[Chern classes|PAD37GKDPD]] and of the [[Hirzebruch–Riemann–Roch theorem|G3X02FKQCR]].\n\n## Explanations\n\n### L1 human\n\nTwo curves in the plane usually meet in finitely many points, and one wants to know how many.\nThe answer is stable only if one counts with multiplicity, works over the complex numbers, and includes points at infinity.\nIntersection theory does this in any dimension, and it allows one to move cycles to general position without changing the answer.\nOn the projective plane, a curve of degree $d$ and a curve of degree $e$ have intersection number $de$.\nThe reason is that each is equivalent to a multiple of a line, and two lines meet in one point.\n",
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