The Milnor number and the Grothendieck's residue

• Grant number: 14/25895-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2015
• End date: November 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Michelle Ferreira Zanchetta Morgado
• Grantee: Mayara Braz Antunes
• 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

Abstract

In the study of critical points of holomorphic functions with isolated critical point, John Milnor introduced an invariant important, which was then called the number of Milnor, presenting interpretations in various areas of Mathematics and has an important role in Singularity Theory. The objective of this work is to present the Milnor number in algebraic point of view and show that it can be interpreted through the residue theory. This is done by studying the Grothendieck's residue, which is a generalization of the Cauchy residue in complex analysis of one variable.