Specialization of integral dependence for modules

• 成果类型: Article
• 署名作者: Gaffney, T; Kleiman, SL
• 署名单位: Northeastern University; Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050335
• 发表日期: 1999
• 页码: 541-574
• 关键词: equisingularity; multiplicities; SINGULARITIES

摘要

We establish the principle of specialization of integral dependence for submodules of finite colength of free modules, as part of the general algebraic-geometric theory of the Buchsbaum-Rim multiplicity. Then we apply the principle to the study of equisingularity of ICIS germs, obtaining results for Whitney's Condition A and Them's Condition A(f). Notably, we describe these equisingularity conditions for analytic families in terms of various numerical invariants, which, for the most part, depend only on the members of a family, not on its total space.