Non-complete algebraic surfaces with logarithmic Kodaira dimension - ∞ and with non-connected boundaries at infinity
Non-complete algebraic surfaces with logarithmic Kodaira dimension - ∞ and with non-connected boundaries at infinity
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具有对数 Kodaira 维数 - ∞ 且无穷远处不连通边界的非完备代数曲面
DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
Shuichiro Tsunoda
中科院分区：
文献类型：
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作者：
M. Miyanishi;Shuichiro Tsunoda
1.设k是特征为p·<$0的代数闭域。设X是定义在k上的代数簇，我们说X是仿射n-规则的，如果X包含一个同构于UX Ak的Zeroki开集，其中U是定义在k上的代数簇，Ak表示k上的一个n-空间。如果X是仿射1-正则的，我们简单地说X是仿射正则的。另一方面，我们说X是仿射无直纹的，如果存在一个支配的拟有限态射：YX使得Y是仿射直纹的，当X是完备的且是仿射直纹的则X是直纹的;如果X是非奇异的射影直纹曲面则X是仿射直纹的。然而，如果X是不完备的，则矿规则性意味着X的更精细的结构，实际上，涉及X的无穷大边界上的数据。更确切地说，我们假定X是非奇异的，我们称三元组（V，D，X）是X的光滑完备化，如果V是k上的非奇异完备簇，D是V上的既约有效因子，其不可约余
1. Let k be an algebraically closed field of characteristic p•†0. Let X be an algebraic variety defined over k, we say that X is affine n-ruled if X contians a Zariski open set isomorphic to UX Ak, where U is an algebraic variety defined over k and Ak denotes the ane n-space over k. If X is affine 1-ruled, we simply say that X is affine-ruled. On the other hand, we say that X is affine-uniruled if there exists a dominant quasi-finite morphism: YX such that Y is affine-ruled, when X is complete and affine-ruled then X is ruled,; if X is a nonsingular projective ruled surface then X is affine-ruled. However, if X is not complete, the mine-ruledness implies a more refined structure of X involving, indeed, the data on the boundary at infinity of X. To be more precise, we assume hereafter that X is nonsingular, we call a triple (V, D, X) a smooth completion of X if V is a nonsingular complete variety over k, D is a reduced effective divisor on V whose irreducible com