On the symmetric subscheme of Hilbert scheme of points
Abstract
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.
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