# nLab Hilbert scheme

Hilbert schemes are moduli spaces of subvarieties of a quasi-projective variety with fixed Hilbert polynomial?. They’re very nice as moduli spaces go, in that they’re actually quasi-projective varieties.

Existence and construction of Hilbert schemes is due Grothendieck (FGA).

The Hilbert scheme of $\mathbb{C}^2$ is widely studied in combinatorics and geometric representation theory for its connections to Macdonald polynomials and Cherednik algebras.

Revised on October 26, 2009 14:25:16 by Zoran Škoda (161.53.130.104)