THE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A HYPERSURFACE WITH ISOLATED SINGULARITY

Autor(es)

Nuno-Ballesteros, J. J. ^[1] ; Orefice-Okamoto, B. ^[2] ; Lima-Pereira, B. K. ^[2] ; Tomazella, J. N. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Valencia, Dept Matemat, Campus Burjassot, Burjassot 46100 - Spain

^[2] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13560905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: QUARTERLY JOURNAL OF MATHEMATICS; v. 71, n. 3, p. 1049-1063, SEP 2020.
• Citações Web of Science: 0

Resumo

Let (X, 0) be an isolated hypersurface singularity defined by phi : (C-n, 0) -> (C, 0) and f : (C-n, 0) -> C such that the Bruce-Roberts number mu(BR)(f, X) is finite. We first prove that mu(BR)(f, X) = mu(f) + mu(phi, f) + mu(X, 0) - t(X, 0), where mu and tau are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety LC(X, 0) is Cohen-Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which the hypersurface (X, 0) was assumed to be weighted homogeneous (AU)

• Processo FAPESP: 16/25730-0 - Invariantes de singularidades determinantais e de aplicações sobre variedades analíticas.
• Beneficiário: Bruna Orefice Okamoto
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/22090-5 - Invariantes de Singularidades
• Beneficiário: João Nivaldo Tomazella
• Modalidade de apoio: Auxílio à Pesquisa - Regular