In characteristic two and dimension two, wild Z/2Z-actions on k[[u,v]] ramified precisely at the origin were classified by Artin, who showed in particular that they induce hypersurface singularities. We introduce in this article a new class of wild quotient singularities in any characteristic p>0 arising from certain non-linear actions of Z/pZ on the formal power series ring in n variables. These actions are ramified precisely at the origin, and their rings of invariants in dimension n=2 are hypersurface singularities, with an equation of a form similar to the form found by Artin when p=2. In higher dimension, the rings of invariants are not local complete intersection in general, but remain quasi-Gorenstein. We establish several structure results for such actions and their corresponding rings of invariants.

中文翻译：

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具有积极特征的中等分支行动

在特征二和维度二中，精确地在原点分叉的 k[[u,v]] 上的野生 Z/2Z 作用被 Artin 分类，他特别表明它们会引起超表面奇点。我们在本文中介绍了一类新的野生商奇点，在任何特征 p>0 中，由 Z/pZ 在 n 变量中的形式幂级数环上的某些非线性作用引起。这些动作在原点精确分枝，它们在 n=2 维上的不变量环是超曲面奇点，其形式类似于 Artin 在 p=2 时发现的形式。在更高维度上，不变量环一般不是局部完全交集，而是保持准 Gorenstein。我们为这些动作及其相应的不变量环建立了几个结构结果。