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Master's Dissertation
DOI
10.11606/D.55.2005.tde-04072005-122826
Document
Author
Full name
Vanda Maria Luchesi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2005
Supervisor
Committee
Atique, Roberta Godoi Wik (President)
Costa, Sueli Irene Rodrigues
Ruas, Maria Aparecida Soares
Title in Portuguese
Invariantes de germes de aplicações de C^2 em C^3
Keywords in Portuguese
cross cap
germes
Invariantes
número de Milnor
pontos duplos
pontos triplos
Abstract in Portuguese
Sejam f:(C^2,0) to (C^3,0) um germe de aplicação holomorfa de coposto 1 e f_t uma perturbação estável de f. Os pontos singulares de f_t são cross-caps, pontos duplos ou pontos triplos. O número de cross-caps e pontos triplos de f_t e o número de Milnor da curva de pontos duplos de f_t são invariantes do germe f. Neste trabalho estudamos fórmulas para obter estes invariantes e no caso dos germes quasi-homogêneos relacionamos estes invariantes com a A_e-codimensão de f.
Title in English
Invariant of map germ from C^2 to C^3
Keywords in English
cross cap
double point
germ
Invariant
Milnor number
triple point
Abstract in English
Let f:(C^2,0) to (C^3,0) be a holomorphic map-germ with corank 1 and f_t a stable perturbation of f. The singular points of f_t are either cross-caps, double points or triple points. The number of cross-caps and the number of triple points of f_t and the Milnor number of the double points curve of f_t are invariants of the germs f. In this work we study formulas to get these invariants and in the case of quasi-homogeneous germs we relate these invariants with the A_e-codimension of f.
 
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dissfinal.pdf (813.65 Kbytes)
Publishing Date
2005-07-18
 
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