 Hilbert scheme (source code)

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= Hilbert scheme
{wiki=Hilbert_scheme}

The Hilbert scheme is an important concept in algebraic geometry that parametrizes subschemes of a given projective variety (or more generally, an algebraic scheme) in a systematic way. More precisely, for a projective variety \\( X \\), the Hilbert scheme \\( \\text\{Hilb\}^n(X) \\) is a scheme that parametrizes all closed subschemes of \\( X \\) with a fixed length \\( n \\).

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