On pencils of curves and deformations of minimally elliptic singularities
On pencils of curves and deformations of minimally elliptic singularities
复制标题
关于曲线铅笔和最小椭圆奇点的变形
DOI：
10.1007/bf01359866
复制
发表时间：
1980
影响因子：
1.4
通讯作者：
U. Karras
中科院分区：
文献类型：
--
作者：
U. Karras
在这篇文章中，我们将研究一类被称为Kodaira奇点的正常曲面奇点--它的解可以通过炸掉一束曲线的奇异纤维点来获得。设~z：M~V是正常曲面奇点(V，p)的一个很好的分解，即例外集A=RT-L(P)的不可约分支是非奇异的且只有正常交点.与7z相关的是一个加权对偶图F，它完全决定了A的拓扑和A嵌入M的可微性，但很少是解析类型。从温特斯[34]的一个定理可以得出，存在与F相关的Kodaira奇点当且仅当f‘满足一个只涉及F给出的数值数据的简单条件，见2.7。这些图称为Kodaira图。正如许多例子所说明的那样，与Kodaira图相关的每个奇点都不是真的Kodaira奇点。
In this paper we shall examine a class of normal surface singularities called Kodaira singularities-whose resolutions can be obtained by blowing up points of the singular fibre of a pencil of curves. We only blow up points on components of multiplicity one of the singular fibre.Let~ z: M~ V be a good resolution of a normal surface singularity (V, p), ie the irreducible components of the exceptional set A= rt-l (p) are non-singular and have only normal crossings. Associated with 7z is a weighted dual graph F which completely determines the topology of A and the differentiable nature of the embedding of A into M, but rarely the analytic type. From a theorem due to Winters [34] it follows that there exists a Kodaira singularity associated to F if and only if f'satisfies a simple condition involving only numerical data given by F, see 2.7. These graphs are called Kodaira graphs. It is not true that each singularity associated to a Kodaira graph is a Kodaira singularity as may be illustrated by many examples.