Equisingularity and the theory of integral closure
The paper is an overview of the author's current approach to equisingularity questions. The notion of landscape of a singularity is introduced as an useful setting for equisingularity problems. The Whitney condition and Verdier's \(W\) regularity, known to be equivalent in the complex analytic case, are efficient tools to say when the members of a family of analytic sets are the same. The theory of integral closure of ideals and modules are introduced to give an algebraic description of these conditions and to provide invariants which control them in families. For the entire collection see [Zbl 1392.58001].
scientific article; zbMATH DE number 7005170