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VOL. 56 | 2009 Smoothness and jet schemes
Shihoko Ishii

Editor(s) Jean-Paul Brasselet, Shihoko Ishii, Tatsuo Suwa, Michel Vaquie


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.


Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1207.14023
MathSciNet: MR2604083

Digital Object Identifier: 10.2969/aspm/05610187

Keywords: arc space, jet schemes

Rights: Copyright © 2009 Mathematical Society of Japan


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