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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2006.tde-24012007-155439
Document
Author
Full name
Michelle Ferreira Zanchetta
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2006
Supervisor
Committee
Saia, Marcelo José (President)
Bedregal, Roberto Callejas
Levcovitz, Daniel
Title in Portuguese
Números de Lê e fórmulas de Lê-Iomdine para germes de hipersuperfícies singulares
Keywords in Portuguese
Ciclos de Lê
Ciclos polares
Hipersuperfícies singulares
Números de Lê
Variedades polares
Abstract in Portuguese
Considerando germes de hipersuperfícies em 'C POT.n+1' com conjunto singular de dimensão s, Massey em [14] introduz um conjunto de (s+1) números chamados de números de Lê. Estes números se mostram como a generalização natural do número de Milnor para singularidades isoladas. O principal objetivo deste trabalho é mostrar como estes números são obtidos e que os números de Lê de uma hipersuperfície singular estão relacionados com os números de Lê de uma certa sequência de hipersuperfícies singulares 'X IND.0',...,'X IND.s-1' que se aproxima da singularidade original de tal forma que os conjuntos críticos de seus termos 'X IND.i' têm dimensão i. Essas relações são dadas pelas fórmulas de Lê-Iomdine.
Title in English
Lê numbers and Lê-Iomdine fórmulas for singular hypersurfaces
Keywords in English
Lê cycles
Lê numbers
Polar cycles
Polar varieties
Singular hypersurfaces
Abstract in English
For any germ of hypersurface in 'C POT. n+1' with singular set of dimension s, Massey in [14] introduces a set of (s+1) numbers called Lê numbers. These numbers are a natural generalization of the Milnor number for isolated singularity hypersurfaces. The main goal of this work is to show how to obtain these numbers and to show the Lê numbers of a singular hypersurface are related with the the Lê numbers of a sequence of singular hypersurfaces 'X IND.0',...,'X IND.s-1' which approach the original singularity in such a way that the critical set of each 'X IND.i' has dimension i. These relationship are given by the Lê-Iomdine formulas.
 
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Revisada.pdf (414.42 Kbytes)
Publishing Date
2007-01-25
 
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