 In the case formula_40, the dimension of formula_18 at formula_42 is greater than or equal to formula_43.In addition to these properties, determined for which polynomials the Hilbert scheme formula_7 is non-empty, and showed that if formula_7 is non-empty then it is linearly connected.So two subschemes of projective space are in the same connected component of the Hilbert scheme if and only if they have the same Hilbert polynomial.