Image Milnor number and A(e)-codimension for maps between weighted homogeneous irreducible curves

Author(s)

Ament, D. A. H. ^[1] ; Nuno-Ballesteros, J. J. ^[2] ; Tomazella, J. N. ^[1]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13560905 Sao Carlos, SP - Brazil

^[2] Univ Valencia, Dept Matemat, Campus Burjassot, Burjassot 46100 - Spain

• Document type: Journal article
• Source: ADVANCES IN GEOMETRY; v. 20, n. 3, p. 319-330, JUL 2020.
• Web of Science Citations: 0

Abstract

Let (X, 0) subset of (C-n, 0) be an irreducible weighted homogeneous singularity curve and let f : (X, 0) -> (C-2, 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of (X, 0). We show that A(e)-codim(X, f) = mu(I)(f), where the A(e)-codimension A(e)-codim(X, f) is the minimum number of parameters in a versal deformation and mu(I)(f) is the image Milnor number, i.e. the number of vanishing cycles in the image of a stabilization of f. (AU)

• FAPESP's process: 16/04740-7 - Invariants of singular varieties and of maps on singular varieties
• Grantee: João Nivaldo Tomazella
• Support Opportunities: Regular Research Grants