Smoothness and jet schemes
Algebraic Geometry
2008-10-28 v1
Abstract
This paper shows some criteria for a scheme of finite type over an algebraically closed field to be non-singular in terms of jet schemes. For the base field of characteristic zero, the scheme is non-singular if and only if one of the truncation morphisms of its jet schemes is flat. For the positive characteristic case, we obtain a similar characterization under the reducedness condition on the scheme. We also obtain by a simple discussion that the scheme is non-singular if and only if one of its jet schemes is non-singular.
Keywords
Cite
@article{arxiv.0810.4571,
title = {Smoothness and jet schemes},
author = {Shihoko Ishii},
journal= {arXiv preprint arXiv:0810.4571},
year = {2008}
}
Comments
12 pages, to appear in Advanced Studies in Pure Math