可能非约化奇点族的代数等分辨性
Algorithmic equiresolution of possibly non-reduced families of singularities
摘要：
本文研究了嵌入簇或理想族的算法等分解的概念，它是指嵌入簇或理想族的同时分解与给定的（适当的）特征零分解算法相容。本文的方法是更间接的：它主要考虑更一般的情况下家庭的基本对象（或标记理想）。提出了算法等分辨的定义，它适用于参数空间T可以是非约化的族，例如，一个合适的Artin环的谱。算法等分辨率的其他定义也进行了讨论。这些在几何上是非常自然的，但是族的参数空间T必须被假定为正则的。证明了当T是正则的时，所有的定义都是等价的.
英文摘要：
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic zero. The paper's approach is more indirect: it primarily considers the more general case of families of basic objects (or marked ideals). A definition of algorithmic equiresolution is proposed, which applies to families whose parameter space T may be non-reduced, e.g., the spectrum of a suitable artinian ring. Other definitions of algorithmic equiresolution are also discussed. These are geometrically very natural, but the parameter space T of the family must be assumed regular. It is proven that when T is regular all the proposed definitions are equivalent.
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