2-step ideals provide a new framework for finding reducible Hilbert schemes and elementary components, producing 215 new examples in dimensions 4, 5 and 6.
Non-reducedness of the Hilbert schemes of few points
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
New components of Hilbert schemes of points and 2-step ideals
2-step ideals provide a new framework for finding reducible Hilbert schemes and elementary components, producing 215 new examples in dimensions 4, 5 and 6.