Palestras e Seminários

05/05/2021

10:30

virtual/à distância

Palestrante: Juan José Nuño Ballesteros

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Responsável: Igor Santos (Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.)

São Carlos Singularity Theory Webinar

Resumo: Let f : (C^n,S) --> (C^n+1,0) be a germ with isolated instability and assume that either f has corank 1 or (n, n + 1) are nice dimensions of Mather. In both cases, there exists a stable perturbation of f whose image in a small enough ball has the homotopy type of a wedge of spheres. The number of such spheres is known as the image Milnor number and is denoted by μI(f). The Mond's conjecture says that μI(f) is greater than or equal to the Ae-codimension of f, with equality if f is weighted homogeneous. This conjecture is known to be true when n = 1, 2 (proved by Mond when n = 1 and independently by Mond and de Jong and van Straten when n = 2) but it remains open for n ≥ 3. In this talk we will show a weak version of the conjecture, namely, that μI(f) = 0 if and only if f is stable (or equivalently, f has Ae-codimension 0). We will present two different proofs, one for the corank 1 case, based on results of Houston about the image computing spectral sequence and another one for the case that (n, n + 1) are nice dimensions, based on the logarithmic characteristic variety of the function which defines the image of a stabilisation of f. We will also discuss some applications of this result.

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