Newton polyhedra and Bruce-Roberts numbers.

• Grant number: 25/11901-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: October 01, 2025
• End date: September 30, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Bruna Orefice Okamoto
• Grantee: Olavo Queiroga de Melo
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Given a hypersurface germ with isolated singularity (X, 0) which is contained in (C^n, 0) and a function germ Rx-finitely determined f defined from (C^n, 0) to C, we will study how to calculate the Bruce-Roberts number of f with respect to X in terms of the Newton polyhedra of f and the function that defines the hypersurface (X, 0). Inspired by the famous Tessier work in which the mu¿star sequence for the Milnor number is defined, we will define a similar one for the Bruce-Roberts number through Bruce-Roberts numbers of f with respect to the generic sections of X. We will study how this sequence relates to equisingularityof families.