论文标题
消失的高级亚历山大型平面曲线不变
Vanishing of Higher Order Alexander-type Invariants of Plane Curves
论文作者
论文摘要
高阶度是对仿射平面曲线的补充的亚历山大型不变性。在本文中，我们表征了这种不变的横向工会的消失，用于$ c'$和$ c''$在有限的方面，$ c'$和$ c''$的消失属性，以及它们是否不可修复。结果，我们表征了这些类型的曲线中的哪种具有琐碎的多变量亚历山大多项式。我们的结果对群体的类别施加了障碍，这些群体可以将其视为曲线横向结合的基本补充基本群体。
The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper we characterize the vanishing of such invariants for transversal unions of plane curves $C'$ and $C''$ in terms of the finiteness, the vanishing properties of the invariants of $C'$ and $C''$, and whether they are irreducible or not. As a consequence, we characterize which of these types of curves have trivial multivariable Alexander polynomial in terms of their defining equations. Our results impose obstructions on the class of groups that can be realized as fundamental groups of complements of a transversal union of curves.
