Invariants associated to map germs

• Grant number: 20/05380-0
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2020
• End date: July 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Michelle Ferreira Zanchetta Morgado
• Grantee: Michelle Ferreira Zanchetta Morgado
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• City of the host institution: São José do Rio Preto
• Associated researchers: Marcelo José Saia ; Roberto Callejas Bedregal

Abstract

In the study of singular complex analytic hypersurfaces from a local point of view, that is, defined by a holomorphic germ, Milnor proves a fibration theorem, obtaining the so-called Milnor fiber (local) associated with this germ. In the case where the hypersurface has an isolated singularity, Milnor introduced an important invariant, now called the Milnor number, which plays an important role in modernSingularity theory. Bruce and Roberts extend Milnor's definition ofa germ number from function f, restricting to a germ of variety X. This number is called the Bruce-Roberts number of f with respect toX. Now, in the case of map germs, being a complete intersection with isolated singularity (ICIS) Hamm proved that this germ also has awell-defined Milnor number associated with it, defined as the degree of middle homology of the corresponding Milnor fiber. In this context, this project searches to extend the number of Bruce-Roberts in the case of map germs F restricted to a variety X, to understand geometric properties of the germ F and X and to obtain results between the Hamm numbers of F and this extension. In addition, the objective is to investigate the behavior of families with respect to this invariant. (AU)