论文标题
有限形态的内部速率
Inner rates of finite morphisms
论文作者
论文摘要
令$（x，0）$为复杂的分析表面细菌，嵌入$（\ mathbb {c}^n，0）$中，具有孤立的奇异性，$φ=（g，f）：（x，0）\ longrightArrow（\ mathbb {c}^2,0）$是有限的。我们定义了一个形态$φ$的分析不变的家族，称为$φ$。通过内部速率，我们研究了与形态$φ$相关的极性曲线，当固定曲线$（gf）^{ - 1}（0）$的拓扑数据和表面胚芽$（x，0）$，从而解决了一个称为极性探索的问题。我们还使用内部速率来研究非恒定全态函数的Milnor纤维的几何形状$ f：（x，0）\ longrightArrow（\ mathbb {c}，0）$。主要结果是一个公式，该公式涉及表面胚芽$（x，0）$的拓扑不变的内部速率和极性曲线以及曲线$（gf）^{ - 1}（0）$。
Let $(X, 0)$ be a complex analytic surface germ embedded in $(\mathbb{C}^n,0)$ with an isolated singularity and $Φ=(g,f):(X,0) \longrightarrow (\mathbb{C}^2,0)$ be a finite morphism. We define a family of analytic invariants of the morphism $Φ$, called inner rates of $Φ$. By means of the inner rates we study the polar curve associated to the morphism $Φ$ when fixing the topological data of the curve $(gf)^{-1}(0)$ and the surface germ $(X,0)$, allowing to address a problem called polar exploration. We also use the inner rates to study the geometry of the Milnor fibers of a non constant holomorphic function $f:(X,0) \longrightarrow (\mathbb{C},0)$. The main result is a formula which involves the inner rates and the polar curve alongside topological invariants of the surface germ $(X,0)$ and the curve $(gf)^{-1}(0)$.
