The Hilbert scheme 
parametrizes closed subschemes of a projective scheme 
having Hilbert
polynomial 
.
It represents the corresponding moduli functor and is itself projective. Hilbert
schemes of points record zero-dimensional subschemes
of a fixed length.
Hilbert Scheme
See also
Hilbert Polynomial, Moduli Space, Scheme, SubschemeExplore with Wolfram|Alpha
References
Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.Cite this as:
Weisstein, Eric W. "Hilbert Scheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HilbertScheme.html