Conformal field theory
The Hilbert space of physical states is a unitary module of the Virasoro algebra corresponding to a fixed value of "c". Stability requires that the energy spectrum of the Hamiltonian be nonnegative. The modules of interest are the highest weight modules of the Virasoro algebra.
Hilbert scheme
Pick a sufficiently large value of . The -dimensional space is a subspace of the -dimensional space , so represents a point of the Grassmannian . This will give an embedding of the piece of the Hilbert scheme corresponding to the Hilbert polynomial into this Grassmannian.