On complex affine surfaces with ℂ+-action
On complex affine surfaces with ℂ+-action
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DOI：
10.1007/bf02564471
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发表时间：
1994-12
影响因子：
0.9
通讯作者：
K. Fieseler
中科院分区：
文献类型：
--
作者：
K. Fieseler
本文的主题是赋予加法群 C+ 的非平凡作用的普通复仿射曲面的分类及其拓扑的某些方面。 Miyanishi 在 [6] 和 [7] 中已经研究了此类表面；一方面从代数的角度来看，通过查看高阶导数的迭代系统（任意特征），另一方面通过研究“类圆柱”仿射曲面，即允许 Z• C 形式的非空开子集的曲面。这里的一个目标是在复杂的情况下完成该图：作为类圆柱曲面，可以从乘积 Z• C、Z 平滑仿射曲线和 C+ 构造法向仿射 C+ 曲面。通过平移作用于第二个因子，通过用“异常纤维”替换纤维化prz：Z•C~Z中的有限数量的轨道。由于仿射曲线 Z 上没有扭曲，因此所得到的表面 V 由特殊纤维中粘合的 C+ 不变邻域的萌芽唯一确定。
The subject of this paper is the classification of normal complex affine surfaces endowed with a nontrivial action of the additive group C+ as well as certain aspects of their topology. Such surfaces have already been studied by Miyanishi in [6] and [7]; on the one hand from an algebraic point of view by looking at iterative systems of higher order derivations (in arbitrary characteritic) and on the other side by investigating" cylinderlike" affine surfaces, ie surfaces which admit non-empty open subsets of the form Z• C.One goal here is to complete that picture in the complex case: As a cylinderlike surface a normal affine C+-surface can be constructed from a product Z• C, Z a smooth affine curve, and C+ acting by translation on the second factor, by replacing in the fibration prz: Z• C~ Z a finite number of orbits by" exceptional fibres". Since there is no twisting over the affine curve Z, the resulting surface V is uniquely determined by the germs of C+-invariant neighbourhoods of the glued in exceptional fibres.