Milnor数与Euler阻塞

函数平方的Lê数及其应用

The Lê numbers of the square of a function and their applications

Lê数由Massey引入，目的是数值控制非孤立超曲面奇点族的拓扑性质，并描述与具有非孤立奇点的函数相关的拓扑。它们是孤立超曲面奇点的Milnor数的推广。本文研究了任意无平方因子的f与$z^2$的复合。他们得到一个公式的合成的Lê数，并考虑这些数字的两个应用。第一个应用是关于满足某些等奇异性条件的函数族中的Lê数不变的程度，第二个应用是关于超曲面奇异性的Euler阻塞的一个新公式的快速证明。几个例子计算使用这个公式，包括任何X定义的函数，只有横向D（q，p）奇点的起源。

Bounded strictly pseudoconvex domains in $\mathbb{C}^2$ with obstruction flat boundary II

On a bounded strictly pseudoconvex domain in $\mathbb{C}^n$, $n>1$, the smoothness of the Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up to the boundary is obstructed by a local CR invariant of the boundary. For a bounded strictly pseudoconvex domain $Ω\subset \mathbb{C}^2$ diffeomorphic to the ball, we prove that the global vanishing of this obstruction implies biholomorphic equivalence to the unit ball, subject to the existence of a holomorphic vector field satisfying a mild approximate tangency condition along the boundary. In particular, by considering the Euler vector …