任意超曲面的阿比扬卡尔-莫半群
Abhyankar-Moh Semigroups for arbitrary hypersurfaces
AI总结：
该研究针对任意超曲面奇点构造了与代数闭域相关的半群，扩展了阿比扬卡尔和莫研究的平面曲线值半群，建立其与根选择无关的条件，还指出其他相关扩展是此构造族的特殊情况。
摘要：
对于任意超曲面奇点，我们构造了一族与代数闭域相关的半群，它们作为级数环的无限并出现。这些半群扩展了阿比扬卡尔和莫所研究的平面曲线的值半群。所考虑的代数闭域具有自然赋值，该赋值诱导出相应的值半群。我们建立了这些半群与根的选择无关的必要条件。此外，P. 冈萨雷斯和基耶克 - 米库斯提出的扩展（其中冈萨雷斯专门处理拟常奇点的情况）以及阿巴斯 - 阿西引入的扩展，可以理解为我们构造的族中的特殊情况。
英文摘要：
For an arbitrary hypersurface singularity, we construct a family of semigroups associated with algebraically closed fields that arise as an infinite union of rings of series. These semigroups extend the value semigroup of a plane curve studied by Abhyankar and Moh. The algebraically closed fields under consideration possess a natural valuation that induces a corresponding value semigroup. We establish the necessary conditions under which these semigroups are independent of the choice of the root. Moreover, the extensions proposed by P. González and Kiyek-Micus, where González specifically addresses the case of quasi-ordinary singularities, and the extension introduced by Abbas-Assi, can be understood as particular instances within our constructed family.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
