标题： 关于映射芽上群作用和映射芽空间 Maps(X,Y) 以及映射箭图的阿廷逼近的进一步结果 显示英文标题

标题： Further results on Artin approximation, for group-actions on mapping-germs Maps(X,Y) and for quivers of maps

摘要： 考虑（解析的，分别代数的）映射芽，Maps((k^n,o),(k^m,o))。这些芽传统上是在右、右和接触等价下进行研究的。下面G是这些群中的一个。在此研究中一个重要工具是Artin逼近：任何映射的正式G等价都可以被普通的（即解析的，分别代数的）G等价逼近。我们考虑具有任意奇点的（解析的，分别代数的）概形芽之间的映射，Maps(X,Y)，并建立该性质（对于G）的更强版本：强Artin逼近和P\l oski逼近。作为初步步骤，我们研究具有奇异目标的映射的接触等价性。在许多情况下，人们使用空间的多芽及其“多映射”。更一般地，“映射芽的图”出现在各种应用中。所需的工具是图的强Artin逼近和P\l oski版本。我们为有根有向树建立了这些结果。 显示英文摘要

摘要： Consider (analytic, resp. algebraic) map-germs, Maps((k^n,o),(k^m,o)). These germs are traditionally studied up to the right, let-right and contact equivalences. Below G is one of these groups. An important tool in this study is the Artin approximation: any formal G-equivalence of maps is approximated by ordinary (i.e. analytic, resp. algebraic) G-equivalence. We consider maps of (analytic, resp. algebraic) scheme-germs, with arbitrary singularities, Maps(X,Y), and establish stronger versions of this property (for G): the Strong Artin approximation and the P\l oski approximation. As a preliminary step we study the contact equivalence for maps with singular targets. In many cases one works with multi-germs of spaces, and with their ``muti-maps". More generally, ``quivers of map-germs" occur in various applications. The needed tools are the Strong Artin approximation for quivers and the P\l oski version. We establish these for directed rooted trees.