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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—Thomas Babington Macaulay (1800–1859)