论文标题
阿波罗尼乌斯的圈子两种方式
Circles of Apollonius two ways
论文作者
论文摘要
由于通常在真实的情况下考虑了阿波罗尼乌斯的问题，所以它遭受了数量的差异：最多八个圆圈与给定的三个圆圈同时是截然不同的，但是有些配置的圆圈少于八个切线。这个问题也是在其他非关闭领域上产生的。使用富集的枚举几何形状的工具，我们提供了两种不同的方法来计算阿波罗尼乌斯的圆圈，以使数字不变性在任何特征的特征领域中都存在。
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio of circles, but some configurations have fewer than eight tangent circles. This issue arises over other non-closed fields as well. Using the tools of enriched enumerative geometry, we give two different ways to count the circles of Apollonius such that invariance of number holds over any field of characteristic not 2. We also pose the geometricity problem for local indices in enriched enumerative geometry.
