On the symmetric subscheme of Hilbert scheme of points

الأصل · EN

We consider the Hilbert scheme Hilbᵈ⁺¹(Cᵈ) of (d+1) points in affine d-space Cᵈ (d > 2), which includes the square of any maximal ideal. We describe equations for the most symmetric affine open subscheme of Hilbᵈ⁺¹(Cᵈ), in terms of Schur modules. In addition we prove that Hilbᵈ⁺¹(Cᵈ) is reducible for n>d>11.