Pathologies on the Hilbert scheme of points
Algebraic Geometry
2019-12-02 v2 Commutative Algebra
Abstract
We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil's Murphy's Law holds up to retraction for this scheme. Our main tool is a generalized version of the Bialynicki-Birula decomposition.
Keywords
Cite
@article{arxiv.1812.08531,
title = {Pathologies on the Hilbert scheme of points},
author = {Joachim Jelisiejew},
journal= {arXiv preprint arXiv:1812.08531},
year = {2019}
}
Comments
24 pages, some explicit examples, comments/questions welcome!