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About: Hilbert scheme     Goto   Sponge   NotDistinct   Permalink

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In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by Alexander Grothendieck. Hironaka's example shows that non-projective varieties need not have Hilbert schemes.