Advanced Studies in Pure Mathematics

Smoothness and jet schemes

Shihoko Ishii

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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

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

Received: 26 March 2008
Revised: 20 August 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document euclid.aspm/1543448018

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Arc space jet schemes


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

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