Variation homological diagrams, and corner singularities (Q5929703)

A general homological framework, the variation arrays and variation homological diagrams, are developed in which corner singularities can be studied from the point of view of duality. A \(k\)-corner singularity is an isolated hypersurface singularity and a set of \(k\) generic hyperplanes, the \(k\)-corner, such that the restriction of this singularity to each intersection of some of these hyperplanes is also an isolated hypersurface singularity. When \(k=1\), the corner singularity is a boundary singularity. As an application, Thom-Sebastiani type properties for isolated singularities are expressed in terms of this framework and established for boundary singularities.