On some birational transformations of the Kummer surface into itself
On some birational transformations of the Kummer surface into itself
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关于库默曲面自身的一些双有理变换
DOI：
10.1090/s0002-9904-1901-00785-9
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发表时间：
1901
影响因子：
1.3
通讯作者：
J. Hutchinson
中科院分区：
文献类型：
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作者：
J. Hutchinson
很少有例子的双有理变换的表面到自己是迄今已知的，其中该集团是无限秩序。具有有限个参数的连续群的情形已经完全解决了，但是对于不连续群，到目前为止只遇到了两三个孤立的例子f。鉴于此，并考虑到对16节四次曲面（即库默曲面）的普遍兴趣，我建议说明如何确定两组无限阶双有理变换，对于这些变换，这些曲面是不变的。首先，我假设曲面是指一个四面体，它的顶点是四个节点，这样选择的四面体的面都不是曲面的奇异切平面。使用齐次坐标w，x，y，z，例如四面体
VERY few examples of the birational transformation of surfaces into themselves are as yet known in which the group is of infinite order. The case of a continuous group with a finite number of parameters has been fully worked out,* but for discontinuous groups only two or three isolated examples f have up to the present time been met with. I t is in view of this, as well as on account of the general interest which attaches to the 16-nodal quartic, or Kummer, surfaces that I propose to show how to determine two groups of birational transformations of infinite order for which these surfaces are invariant. In the first place I suppose the surface to be referred to a tetrahedron whose vertices are four nodes so chosen that none of the faces of the tetrahedron are singular tangent planes of the surface. Using homogeneous coordinates w, x, y, z, take for example the tetrahedron