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  "body": "\n## Definition\n\n*Enumerative geometry* is the branch of algebraic geometry that determines the number of geometric objects of a given kind that satisfy given conditions.\nThe objects are typically subvarieties of [[projective space|ZT9A6JK8QF]], such as lines, conics or rational curves.\nThe conditions are chosen in general position, and an answer is a number that is the same for all general choices.\nA standard method treats the objects as points of a [[moduli space|FJZRW9P0K3]] and each condition as a subvariety.\nThe count is then an [[intersection number|4HV4WTAX9P]].\n\n## Remarks\n\nExample: in $\\mathbb{P}^3$, exactly $2$ lines meet four lines in general position.\nIn the Grassmannian of lines, each condition is a hypersurface, and the product of four such classes is $2$ times the class of a point.\n\nExample: there are $3264$ smooth conics in $\\mathbb{P}^2$ tangent to five general conics.\nSteiner gave the answer $7776$, which counts degenerate double lines as well, and the correct number $3264$ is due to Chasles.\n\nNon-example: the number of lines meeting four lines that all lie in one plane is infinite.\nEvery line in that plane meets all four, so the conditions are not in general position.\n\nOther classical numbers are $27$ lines on a smooth cubic surface and $2875$ lines on a general quintic threefold.\n",
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