2023/09/28 by Alberto Fernández-Hernández, Fernández-Hernández, Alberto, J. J. Nuño‐Ballesteros +1
Mathematics · #58K40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 58K15 #Secondary 32S30
paper · pdf · doi:10.48550/arxiv.2309.16193
openalex publication_date 2023/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study germs of hypersurfaces (Y,0)⊂ (\mathbb Cn+1,0) that can be described as the image of \mathscr A-finite mappings f:(X,S)→ (\mathbb Cn+1,0) defined on an ICIS (X,S) of dimension n. We extend the definition of the Jacobian module given by Fernández de Bobadilla, Nuño-Ballesteros and Peñafort-Sanchis when X=\mathbb Cn, which controls the image Milnor number μI(X,f). We apply these results to prove the case n=2 of the generalised Mond conjecture, which states that μI(X,f)≥ codim\mathscr Ae (X,f), with equality if (Y,0) is weighted homogeneous.