We say that a group G of local (maybe formal) biholomorphisms satisfies the uniform intersection property if the intersection multiplicity $(\phi (V), W)$ takes only finitely many values as a function of G for any choice of analytic sets V and W of complementary dimension. In dimension $2$ we show that G satisfies the uniform intersection property if and only if it is finitely determined – that is, if there exists a natural number k such that different elements of G have different Taylor expansions of degree k at the origin. We also prove that G is finitely determined if and only if the action of G on the space of germs of analytic curves has discrete orbits.

我们说，如果对于任何分析集 V 的选择，交集多重性 $(\phi (V), W)$ 仅将有限多个值作为 G的 函数 ，则一组局部（可能是形式的）双全同态满足一致交集性质 和W的互补尺寸。在维度 $2$ 中，我们证明G满足均匀交集性质当且仅当它是有限确定的——也就是说，如果存在一个自然数k使得G的不同元素在原点具有不同的k度泰勒展开式。我们还证明了G是有限确定的当且仅当G对解析曲线的细菌空间的作用具有离散轨道。