Singularities of normal affine surfaces containing cylinderlike open sets
Singularities of normal affine surfaces containing cylinderlike open sets
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包含类圆柱开集的法线仿射曲面的奇点
DOI：
10.1016/0021-8693(81)90264-7
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发表时间：
1981
影响因子：
0.9
通讯作者：
M. Miyanishi
中科院分区：
文献类型：
--
作者：
M. Miyanishi
设k是一个特征为零的代数闭域，本文将其作为基域。设X是定义在k上的法向afline曲面。X的开集U称为类圆柱开集，如果iJ同构于IJ，，xAi，其中Ui是曲线，AL表示直线.若给定加群概型G在正规仿射曲面X上的一个非平凡作用，则已知X包含一个类圆柱开集（参见图1）。Miyanishi和Nakai [8; Theorem，p. 151）.本文的目的是证明：如果正规仿射曲面X包含一个类圆柱开集，则X的每个奇点都是有理奇点（参见Artin [1]），并刻画了这种有理奇点。
Let k be an algebraically closed field of characteristic zero, which we fix as the ground field throughout this paper. Let X be a normal afline surface defined over k. An open set U of X is said to be a cylinderlike open set if iJ is isomorphic to IJ,, x Ai, where U, is a curve and AL denotes the alline line. If there is given a nontrivial action of the additive group scheme G, on a normal afftne surface X then it is known that X contains a cylinderlike open set (cf. Miyanishi and Nakai [8; Theorem, p. 151). The purpose of the present article is to show that if a normal afftne surface X contains a cylinderlike open set every singular point of X is a rational singular point (cf. Artin [l]), and to characterize such rational singular points.