Modules of Derivations, Logarithmic Ideals and Singularities of Maps on Analytic Varieties

Autor(es)

Bivia-Ausina, Carles ; Kourliouros, Konstantinos ; Ruas, Maria Aparecida Soares

• Tipo de documento: Artigo Científico
• Fonte: Results in Mathematics; v. 80, n. 5, p. 35-pg., 2025-08-01.

Resumo

We introduce the module of derivations Theta h,M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta _{h,M}$$\end{document} attached to a given analytic map h:(Cn,0)->(Cp,0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h:({\mathbb {C}}<^>n,0)\rightarrow ({\mathbb {C}}<^>p,0)$$\end{document} and a submodule M subset of Onp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\subseteq {\mathcal {O}}_n<^>p$$\end{document} and analyse several exact sequences related to Theta h,M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta _{h,M}$$\end{document}. Moreover, we obtain formulas for several numerical invariants associated to the pair (h, M) and a given analytic map germ f:(Cn,0)->(Cq,0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:({\mathbb {C}}<^>n,0)\rightarrow ({\mathbb {C}}<^>q,0)$$\end{document}. In particular, if X is an analytic subvariety of Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}<^>n$$\end{document}, we derive expressions for analytic invariants defined in terms of the module Theta X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta _X$$\end{document} of logarithmic vector fields of X. (AU)

• Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Temático