Non-reducedness of the Hilbert schemes of few points

Abstract

We use generalised Bialynicki-Birula decomposition, apolarity and obstruction theories to prove non-reducedness of the Hilbert scheme of $13$ points on ${\mathbb{A}}^6$. Our argument doesn't involve computer calculations and gives an example of a fractal-like structure on this Hilbert scheme.

40 pages, after corrections

Cited by in corpus (1)

• Rational singularities of nested Hilbert schemes