## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 187 - 199

### Smoothness and jet schemes

#### 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.

#### Article information

**Dates**

Received: 26 March 2008

Revised: 20 August 2008

First available in Project Euclid:
28 November 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1543448018

**Digital Object Identifier**

doi:10.2969/aspm/05610187

**Mathematical Reviews number (MathSciNet)**

MR2604083

**Zentralblatt MATH identifier**

1207.14023

**Keywords**

Arc space jet schemes

#### Citation

Ishii, Shihoko. Smoothness and jet schemes. Singularities — Niigata–Toyama 2007, 187--199, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610187. https://projecteuclid.org/euclid.aspm/1543448018