Smooth Hilbert schemes: their classification and geometry
Algebraic Geometry
2023-01-13 v2 Commutative Algebra
Abstract
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is smooth. We also reinterpret these smooth Hilbert schemes as generalized partial flag varieties and describe the subschemes being parametrized.
Keywords
Cite
@article{arxiv.2008.08938,
title = {Smooth Hilbert schemes: their classification and geometry},
author = {Roy Skjelnes and Gregory G. Smith},
journal= {arXiv preprint arXiv:2008.08938},
year = {2023}
}
Comments
21 pages, v2 improves the exposition and corrects minor errors