NON-NEGATIVE DEFORMATIONS OF WEIGHTED HOMOGENEOUS SINGULARITIES

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Univ Valencia, Dept Geometria & Topol, Campus Burjassot, E-46100 Burjassot - Spain

^[2] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13560 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Glasgow Mathematical Journal; v. 60, n. 1, p. 175-185, JAN 2018.
• Citações Web of Science: 2

Resumo

We consider a weighted homogeneous germ of complex analytic variety (X, 0) subset of (C-n, 0) and a function germ f : (C-n, 0) -> (C, 0). We derive necessary and sufficient conditions for some deformations to have non-negative degree (i.e., for any additional term in the deformation, the weighted degree is not smaller) in terms of an adapted version of the relative Milnor number. We study the cases where (X, 0) is an isolated hypersurface singularity and the invariant is the Bruce-Roberts number of f with respect to (X, 0), and where (X, 0) is an isolated complete intersection or a curve singularity and the invariant is the Milnor number of the germ f : (X, 0) -> C. In the last part, we give some formulas for the invariants in terms of the weights and the degrees of the polynomials. (AU)

• Processo FAPESP: 13/14014-3 - Equisingularidade de variedades determinantais
• Beneficiário: Bruna Orefice Okamoto
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/10856-0 - Equisingularidade e invariantes de singularidades
• Beneficiário: João Nivaldo Tomazella
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/08877-3 - Número de Milnor, número de Bruce-Roberts e variedades determinantais
• Beneficiário: Bruna Orefice Okamoto
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado