Note on the degree of Cº-sufficiency of plane curves.

Antonio F. Costa

Publicacions Matemàtiques (1989)

  • Volume: 33, Issue: 1, page 37-46
  • ISSN: 0214-1493

Abstract

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Let f be a germ of plane curve, we define the δ-degree of sufficiency of f to be the smallest integer r such that for anuy germ g such that j(r) f = j(r) g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the δ-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the δ-degree of sufficiency is equal to the Cº-degree of sufficiency.

How to cite

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Costa, Antonio F.. "Note on the degree of Cº-sufficiency of plane curves.." Publicacions Matemàtiques 33.1 (1989): 37-46. <http://eudml.org/doc/41065>.

@article{Costa1989,
abstract = {Let f be a germ of plane curve, we define the δ-degree of sufficiency of f to be the smallest integer r such that for anuy germ g such that j(r) f = j(r) g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the δ-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the δ-degree of sufficiency is equal to the Cº-degree of sufficiency.},
author = {Costa, Antonio F.},
journal = {Publicacions Matemàtiques},
keywords = {Curvas planas; Invariantes; Suficiencia; Isotopía; delta-degree of sufficiency; germ of plane curves; delta-equivalent; C sub 0 degree of sufficiency},
language = {eng},
number = {1},
pages = {37-46},
title = {Note on the degree of Cº-sufficiency of plane curves.},
url = {http://eudml.org/doc/41065},
volume = {33},
year = {1989},
}

TY - JOUR
AU - Costa, Antonio F.
TI - Note on the degree of Cº-sufficiency of plane curves.
JO - Publicacions Matemàtiques
PY - 1989
VL - 33
IS - 1
SP - 37
EP - 46
AB - Let f be a germ of plane curve, we define the δ-degree of sufficiency of f to be the smallest integer r such that for anuy germ g such that j(r) f = j(r) g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the δ-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the δ-degree of sufficiency is equal to the Cº-degree of sufficiency.
LA - eng
KW - Curvas planas; Invariantes; Suficiencia; Isotopía; delta-degree of sufficiency; germ of plane curves; delta-equivalent; C sub 0 degree of sufficiency
UR - http://eudml.org/doc/41065
ER -

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