Equisingularity, Multiplicity, and Dependence
Abstract
This is a report on some recent work by Gaffney, Massey, and the author, characterizing the conditions Af and Wf for a family of ICIS germs equipped with a function. First we introduce the work informally. Then we review the formal definitions of Af and Wf, 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.