Abstract

In this exposition, we propose a notion of rank and rigidity of locally nilpotent derivations of affine fibrations. We show that the concept is analogous to the perception of rank and rigidity of locally nilpotent derivations of polynomial algebras. Our results characterize locally nilpotent derivations of ${\mathbb{A}}^3$-fibrations having slice by classifying the fixed point free locally nilpotent derivations in terms of their ranks.

中文翻译：

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仿射纤维的局部幂零推导的秩和刚性

摘要

在这个说明中，我们提出了仿射纤维的局部幂零推导的秩和刚性的概念。我们表明该概念类似于多项式代数的局部幂零推导的秩和刚性的感知。我们的结果表征了局部幂零推导${\mathbb{一种}}^3$-fibrations 通过根据等级对无不动点的局部幂零推导进行分类而具有切片。