English

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

R2 v1 2026-06-21T11:34:47.710Z