TOPOLOGICAL TRIVIALITY OF LINEAR DEFORMATIONS WITH CONSTANT LE NUMBERS

Autor(es)

Eyral, Christophe ^[1] ; Ruas, Maria Aparecida Soares ^[2]

Afiliação do(s) autor(es)

^[1] Polskiej Akad Nauk, Inst Matemat, Ul Sniadeckich 8, PL-00656 Warsaw - Poland

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400 Ctr, BR-13566590 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: KODAI MATHEMATICAL JOURNAL; v. 39, n. 1, p. 189-201, MAR 2016.
• Citações Web of Science: 1

Resumo

Let f (t, z) = f(0) (z) + tg(z) be a holomorphic function defined in a neighbourhood of the origin in C x C-n. It is well known that if the one-parameter deformation family [f(t)] defined by the function f is a mu-constant family of isolated singularities, then [f(t)] is topologically trivial a result of A. Parusinski. It is also known that Parusinski's result does not extend to families of non-isolated singularities in the sense that the constancy of the Le numbers of f(t) at 0, as t varies, does not imply the topological triviality of the family [f(t)] in general a result of J. Fernandez de Bobadilla. In this paper, we show that Parusinski's result generalizes all the same to families of non isolated singularities if the Le numbers of the function f itself are defined and constant along the strata of an analytic stratification of C x (f(0)(-1)(0) boolean AND g(-1)(0)). Actually, it suffices to consider the strata that contain a critical point of f. (AU)

• Processo FAPESP: 14/00304-2 - Singularidades de aplicações diferenciáveis: teoria e aplicações
• Beneficiário: Maria Aparecida Soares Ruas
• Modalidade de apoio: Auxílio à Pesquisa - Temático