Smoothness and jet schemes
Smoothness and jet schemes
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DOI：
10.2969/aspm/05610187
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发表时间：
2008-10
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影响因子：
--
通讯作者：
S. Ishii
中科院分区：
文献类型：
--
作者：
S. Ishii
本文给出了代数闭域上的有限型格式在JET格式意义下非奇异的一些判据。对于特征为零的基场，该格式是非奇异的当且仅当其JET格式的一个截断态射是平坦的。对于正特征情形，我们在约化条件下得到了类似的刻画。通过简单的讨论，我们还得到了该格式非奇异的充要条件是它的一个JET格式是非奇异的。
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.