A weak version of the Mond conjecture
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Giménez Conejero, R.
[2]
;
Nuño-Ballesteros, J. J.
[1]
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[1] Universitat de València
Universitat de València
Valencia, España
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[2] Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, 1053, Hungary
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 753-770
- Idioma: inglés
- DOI: 10.1007/s13348-023-00411-x
- Enlaces
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Resumen
We prove that a map germ f:(C,S) - (Cn +, 0) with isolated instability is stable if and only if ui(f)= 0, where ui (f) is the image Milnor number defined by Mond. In a previous paper we proved this result with the additional assumption that f has corank one. The proof here is also valid for corank > 2, provided that (n,n +1) are nice dimensions in Mather’s sense (so ui (f) is well defined). Our result can be seen as a weak version of a conjecture by Mond, which says that the Ae-codimension of f is < ui(f), with equality if f is weighted homogeneous. As an application, we deduce that the bifurcation set of a versal unfolding of f is a hypersurface.
