Elementary components of Hilbert schemes
Algebraic Geometry
2019-04-09 v5 Commutative Algebra
Abstract
We generalize the Bialynicki-Birula decomposition to singular schemes and apply it to the Hilbert scheme of points on an affine space. We find an infinite family of small, elementary and generically smooth components of the Hilbert scheme of points of the affine four-space. Our method gives easily verifiable sufficient conditions for proving that a point of the Hilbert scheme is smooth and lies on an elementary component. We also present a necessary condition for smoothability of a finite subscheme given by a homogeneous ideal.
Cite
@article{arxiv.1710.06124,
title = {Elementary components of Hilbert schemes},
author = {Joachim Jelisiejew},
journal= {arXiv preprint arXiv:1710.06124},
year = {2019}
}
Comments
post-final version, corrected proof of Thm 4.9