二维双全纯作用的相交数的有界性
Boundness of intersection numbers for actions by two-dimensional biholomorphisms
摘要：
我们说一个局部（可能是形式的）双全纯的群$G$满足一致交性质，如果对于任意选择的解析集$V$和$W$，交重数$(ϕ(V), W)$只取100个值作为$G$的函数。在$2$维中，我们证明了$G$满足一致交性质当且仅当它是可确定的，即存在一个自然数$k$，使得$G$的不同元素在原点有不同程度的泰勒展开式$k$.我们还证明了$G$是非确定的当且仅当$G$在解析曲线芽空间上的作用具有离散轨道。
英文摘要：
We say that a group $G$ of local (maybe formal) biholomorphisms satisfies the uniform intersection property if the intersection multiplicity $(ϕ(V), W)$ takes only finitely many values as a function of $G$ for any choice of analytic sets $V$ and $W$. In dimension $2$ we show that $G$ satisfies the uniform intersection property if and only if it is finitely determined, i.e. 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 have discrete orbits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
