平等性、多重性和依赖性
Equisingularity, Multiplicity, and Dependence
摘要：
本文是Gaffney，Massey和作者最近工作的一个报告，描述了一类具有函数的ICIS芽的条件A_f和W_f。首先，我们非正式地介绍工作。然后回顾了A_f和W_f的形式定义，并给出了用Milnor数的恒常性刻画它们的定理。接下来我们回顾了Buchsbaum-Rim重数的定义，并通过某些Buchsbaum-Rim重数的恒定性重新表述了定理。最后，我们回顾了元素对自由模的子模的积分依赖理论，并应用它证明了改进的定理。
英文摘要：
This is a report on some recent work by Gaffney, Massey, and the author, characterizing the conditions A_f and W_f for a family of ICIS germs equipped with a function. First we introduce the work informally. Then we review the formal definitions of A_f and W_f, and state the theorems that characterize them by the constancy of Milnor numbers. Next we review the definition of the Buchsbaum-Rim multiplicity, and reformulate the theorems by the constancy of certain Buchsbaum-Rim multiplicities. Finally, we review the theory of integral dependence of elements on submodules of free modules, and apply it to prove the reformulated theorems.
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。
