Resolution of corank 1 singularities of a generic front (Q1428947)

The author obtains a resolution of singularities for wave fronts having only stable singularities of corank \(1\). This resolution is based on a transformation that takes a given front to a new front with singularities of the same type in a space of smaller dimension. This transformation is defined by the class \(A_\mu\) of Legendre singularities. The front and the ambient space obtained by the \(A_\mu\)-transformation inherit topological information on the closure of the manifold of singularities \(A_\mu\) of the original front. The resolution of every (reducible) singularity of a front is determined by a suitable iteration of \(A_\mu\)-transformations. As a corollary, the author obtains new conditions for the coexistence of singularities of generic fronts.