Higher-dimensional analogues of periodic continued fractions and cusp singularities
Higher-dimensional analogues of periodic continued fractions and cusp singularities
复制标题
周期性连续分数和尖点奇点的高维类似物
DOI：
--
复制
发表时间：
1983
期刊：
影响因子：
--
通讯作者：
Hiroyasu Tsuchihashi
中科院分区：
文献类型：
--
作者：
Hiroyasu Tsuchihashi
导论.在周期连分式和二维尖点奇点之间有一个众所周知的关系。(See，例如，[10]，[11]。）设π：U→V是二维尖点奇点（V，p）的最小分解。则例外集X=π-1（p）或者是s条有理曲线的圈，其自交数为a1，a2，.，作为n-2，其中至少有一个严格小于-2（s n-2），或具有节点和自相交数a<0的有理曲线。然后我们可以把周期连分数和它联系起来
Introduction. There is a well-known relationship between periodic continued fractions and 2-dimensional cusp singularities. (See, for instance, [10], [11].) Let π: U→V be the minimal resolution of a 2dimensional cusp singularity (V,p). Then the exceptional set X=π-1(p) is either a cycle of s rational curves with self-intersection numbers a1, a2, ..., as≦-2 at least one of which is strictly smaller than -2(s≧2), or a rational curve with a node and with a self-intersection number a<0. Then we can associate to it the periodic continued fraction