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 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 1961).
Read more about Hilbert Scheme: Hilbert Scheme of Projective Space, Hilbert Scheme of Points On A Manifold, Hilbert Schemes and Hyperkähler Geometry
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“We doubt not the destiny of our country—that she is to accomplish great things for human nature, and be the mother of a nobler race than the world has yet known. But she has been so false to the scheme made out at her nativity, that it is now hard to say which way that destiny points.”
—Margaret Fuller (1810–1850)