In embedding dimension five, the one-step loci with Hilbert function (1,5,r) are contained in the smoothable component for all r except 3 and 5, which form the generically reduced elementary components.
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The one-step Shafarevich gap in embedding dimension five
In embedding dimension five, the one-step loci with Hilbert function (1,5,r) are contained in the smoothable component for all r except 3 and 5, which form the generically reduced elementary components.