论文标题
圆形包装和理想班级组的几何研究
A geometric study of circle packings and ideal class groups
论文作者
论文摘要
为每个虚构的二次场$ k $介绍了一个圆圈的分形系列。总的来说，这些布置包含（直至仿射变换）具有积分曲线和Zariski致密对称组的扩展复合平面中的每组圆。当该集合是一个圆形填料时，我们会展示安排的环境结构如何提供几何标准，以满足几乎局部的全球原理。还探索了与$ K $的类的连接。其中的几何特性保证某些理想类是组发电机。
A family of fractal arrangements of circles is introduced for each imaginary quadratic field $K$. Collectively, these arrangements contain (up to an affine transformation) every set of circles in the extended complex plane with integral curvatures and Zariski dense symmetry group. When that set is a circle packing, we show how the ambient structure of our arrangement gives a geometric criterion for satisfying the almost local-global principle. Connections to the class group of $K$ are also explored. Among them is a geometric property that guarantees certain ideal classes are group generators.
