Equisingular generic discriminants and Whitney conditions

Eric Dago Akéké[1]

  • [1] UFR de Mathématiques et d’Informatique, Université d’Abidjan-Cocody, 21 BP 3821 Abidjan 21 (Côte d’Ivoire)

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 4, page 661-671
  • ISSN: 0240-2963

Abstract

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The purpose of this article is to show that the Whitney conditions are satisfied for complex analytic families of normal surface singularities for which the generic discriminants are equisingular. According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of minimal normal surface singularities these two equisingularity conditions are equivalent.

How to cite

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Dago Akéké, Eric. "Equisingular generic discriminants and Whitney conditions." Annales de la faculté des sciences de Toulouse Mathématiques 17.4 (2008): 661-671. <http://eudml.org/doc/10100>.

@article{DagoAkéké2008,
abstract = {The purpose of this article is to show that the Whitney conditions are satisfied for complex analytic families of normal surface singularities for which the generic discriminants are equisingular. According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of minimal normal surface singularities these two equisingularity conditions are equivalent.},
affiliation = {UFR de Mathématiques et d’Informatique, Université d’Abidjan-Cocody, 21 BP 3821 Abidjan 21 (Côte d’Ivoire)},
author = {Dago Akéké, Eric},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {equisingularity; discriminant; Whitney conditions; minimal surface singularity},
language = {eng},
month = {6},
number = {4},
pages = {661-671},
publisher = {Université Paul Sabatier, Toulouse},
title = {Equisingular generic discriminants and Whitney conditions},
url = {http://eudml.org/doc/10100},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Dago Akéké, Eric
TI - Equisingular generic discriminants and Whitney conditions
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 4
SP - 661
EP - 671
AB - The purpose of this article is to show that the Whitney conditions are satisfied for complex analytic families of normal surface singularities for which the generic discriminants are equisingular. According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of minimal normal surface singularities these two equisingularity conditions are equivalent.
LA - eng
KW - equisingularity; discriminant; Whitney conditions; minimal surface singularity
UR - http://eudml.org/doc/10100
ER -

References

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  4. Bondil (R.).— Fine polar invariants of minimal singularities of surfaces. preprint, Arxiv: AG/0401434 (2004). 
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  20. Zariski (O.).— Studies in equisingularity, equivalent singularities of plane algebroid curves. Amer. J. Math., 87 (1965). Zbl0132.41601

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