2025/05/12 by C. Muñoz-Cabello, Muñoz-Cabello, C., J. J. Nuño‐Ballesteros +3
Mathematics · #58K60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Primary 32S30 #Secondary 32S25
paper · pdf · doi:10.48550/arxiv.2505.07644
openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We give a formula to count the number of D4 singularities in a stable frontal perturbation of a corank 2 wave front singularity f\colon (ℂ3,0) → (ℂ4,0) using Mond's method of stable perturbations of map germs. For a generic germ of corank 2 wave front f\colon (ℂ3,S) → (ℂ4,0), the image of a stable deformation ft of f exhibits Ak singularities with k ≤ 4, their transverse intersections and the aforementioned D4 singularities for 0 < |t| ≪ 1. By interpreting the image of ft as the discriminant (the image of the critical point set) of a smooth map germ Ht\colon (ℂ5,0) → (ℂ4,0), we define an algebra whose dimension over ℂ is equal to the number of D4 points in the image of ft.