Isotrivial Families of Curves on Affine Surfaces and Characterization of the Affine Plane
Isotrivial Families of Curves on Affine Surfaces and Characterization of the Affine Plane
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仿射曲面上的等平凡曲线族及仿射平面的表征
DOI：
10.1070/im1988v030n03abeh001027
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. Zaidenberg
中科院分区：
文献类型：
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作者：
M. Zaidenberg
主要结果是C2是一个光滑的无环代数曲面，其上存在单连通代数曲线（可能是奇异的和可约的）或等平凡（非例外）曲线族，特别是，这样的曲线和族不能存在于Ramanujam曲面上-拓扑可收缩的光滑代数曲面与C2不同构。该证明基于一个结构定理，该结构定理描述了几何单阶具有有限阶的曲线族的退化纤维。运用双曲复合体分析技术；C*团的常规活动起着重要的作用。参考书目：40篇。
The main result is a characterization of C2 as a smooth acyclic algebraic surface on which there exist simply connected algebraic curves (possibly singular and reducible) or isotrivial (nonexceptional) families of curves with base C. In particular, such curves and families cannot exist on Ramanujam surfaces — topologically contractible smooth algebraic surfaces not isomorphic to C2. The proof is based on a structure theorem which describes the degenerate fibers of families of curves whose geometric monodromy has finite order. Techniques of hyperbolic complex analysis are used; an important role is played by regular actions of the group C*. Bibliography: 40 titles.